Download Growth and characterisation of Bi-based multiferroic thin films Eric Langenberg Pérez

Growth and characterisation of Bi-based
multiferroic thin films
Eric Langenberg Pérez
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Growth and characterisation of Bi-based
multiferroic thin films
Eric Langenberg Pérez
PhD thesis
Memòria presentada per a l’obtenció del grau de Doctor per la Universitat de Barcelona
en el marc del programa de Doctorat en Física
Directors:
Dr. Manuel Varela Fernández
Dr. Josep Fontcuberta i Griñó
Departament de Física Aplicada i Òptica, Facultat de Física
Universitat de Barcelona
Juny 2013
Abstract
Multiferroic materials, in which both ferroelectric and (anti)ferromagnetic orders
coexist in the same phase, have received much interest in the last few years. The
possibility of these two ferroic orders being coupled allows new functionalities in these
materials as controlling the magnetisation by an electric field or, conversely, controlling
the polarisation by a magnetic field. The fulfilment of this magnetoelectric coupling is
not only interesting in terms of fundamental research but it would also pave the way for
designing novel magnetoelectric applications, especially in the field of spintronics, like
spin filters or magnetic tunnel junctions controlled by electric fields instead of using
magnetic fields, and thus promoting a new generation of high-density and low-powerconsumption storage devices. For this latter purpose, ferromagnetic multiferroics would
have greater advantages over the antiferromagnetic ones because of the net
magnetisation, which would allow an easier control of the magnetic state. However, it is
the antiferromagnetic order which prevails in multiferroic materials; hence, research
focused on identification of new ferromagnetic ferroelectrics is needed.
Bi-based perovskite and double-perovskite oxides, BiBO3 and Bi2 BB’O6,
respectively, where B and B’ are magnetic transition metal ions (i.e. with a partially
occupied outer electron d shell), present an excellent starting point to investigate new
ferromagnetic ferroelectric materials. In these compounds ferroelectricity arises from
the stereochemical activity of Bi3+ cations. The outer electrons of the 6s orbitals of Bi3+,
called lone pairs, do not participate in chemical bonds. When surrounded by the oxygen
anions they off-centre from the centrosymmetric position due to the Coulombian
electrostatic repulsion, forming an electric dipole and breaking the spatial inversion
symmetry (the required condition, though not sufficient, for ferroelectric order to
occur). Conversely, magnetism is driven by the superexchange interaction between the
magnetic ions, i.e. B-cations, through the adjacent oxygen ions (B – O – B). Whether
superexchange interaction is ferromagnetic or antiferromagnetic depends, to a large
extent, on the electronic configuration of the d orbitals of B cations, which in
perovskites splits into high-energy eg orbitals and low-energy t2g orbitals. In an ideal
perovskite in which B – O – B bond angle is 180º, either B (empty eg orbitals) – O – B
(empty eg orbitals) or B (half-filled eg orbitals) – O – B (half-filled eg orbitals)
i
configurations give rise to antiferromagnetic interactions, whereas B (half-filled eg
orbitals) – O – B (empty eg orbitals) configuration gives rise to ferromagnetic
interactions. As the B-site is occupied by only one kind of ion in perovskite oxides and,
in general, with the same oxidation state, i.e. having the same eg orbital filling,
antiferromagnetic interactions are much more common than the ferromagnetic ones.
Instead, by appropriately choosing the B – B’ cations in double-perovskite oxides,
ferromagnetic superexchange interactions can be designed. Hence, Bi-based doubleperovskite oxides provide the possibility of engineering long-range ferromagnetism (as
long as B – B’ – B – B’ – ... long-range B-site order is accomplished) and consequently
overcoming the scarcity of ferromagnetic multiferroics.
In particular, to date, BiMnO3 and Bi2NiMnO6 systems are the only reported
ferromagnetic Bi-based perovskite oxides, possessing a magnetic Curie temperature
around 105 K and 140 K, respectively, in bulk form. Additionally, they are promising
candidates to display ferroelectricity driven by the aforementioned stereochemical
activity of Bi cations and, hence, both systems are investigated in the work of this thesis
in thin films.
First of all, this thesis addresses the synthesis of these compounds. In this process,
three main hindrances were met. Firstly, these Bi-based compounds are highly
metastable, which implies that they are only possible to be synthesised in bulk under
extreme conditions, i.e. under high temperatures and high pressures (around 5 GPa).
The strategy used to circumvent the required high pressures consisted of replacing the
mechanical pressure by the epitaxial stress in thin films, i.e. using substrates whose
crystal lattice parameters show a low mismatch with those of the compound that is to be
formed. For this purpose these Bi-based compounds were grown by pulsed laser
deposition (PLD) onto single-crystal (001)-oriented SrTiO3 substrates. Secondly, Bi is a
highly volatile element and consequently the synthesis temperature was not a free
deposition parameter, forcing the use of low synthesis temperatures in order to prevent
non-stoichiometric films or even the no-formation of the compound when the Bideficiency was too large. Yet the general metastable character of these compounds
demands the use of high temperatures to the synthesis process. These two antagonistic
requirements were tried to be balanced by using 10% Bi-rich PLD targets in the case of
BiMnO3 system and by partial replacement of Bi3+ cations by La3+ cations (by 10%) in
the case of Bi2NiMnO6 system. In the latter approach, La-doping gives rise to a slightly
ii
reduced unit cell volume, exerting the so-called chemical pressure (equivalently to a
hydrostatic pressure) which contributes to prevent Bi3+ cations from desorption during
the growth process. Thirdly, both in the ternary Bi – Mn – O and quaternary Bi – Ni –
Mn – O systems a strong multiphase formation tendency was found, especially in the
former, in which apart from the desired BiMnO3 and Bi2NiMnO6 compounds, different
parasitic oxide phases like Mn3O4, Bi2O3 and MnO2 for the former system and NiO for
the latter system appeared in the grown films. As a consequence of all these facts the
single-phase stabilisation of either BiMnO3 or (Bi0.9La0.1)2NiMnO6 was greatly
hampered and only possible to be achieved under a narrow window of deposition
conditions. Especially critical was the temperature deposition window, which was
required to be as narrow as 10ºC around 630ºC and 620ºC for BiMnO3 and
(Bi0.9La0.1)2NiMnO6 synthesis, respectively.
Once the deposition conditions for single-phase stabilisation of the Bi-based
compounds are controlled, structural characterisation proves that both BiMnO3 and
(Bi0.9La0.1)2NiMnO6
grow
fully
coherent
(compressive
and
tensile
strained,
respectively) on SrTiO3 substrates, thus adopting as the in-plane lattice parameter that
of the cubic substrate and subsequently a tetragonal-like structure. Importantly enough
for the magnetic properties, (Bi0.9La0.1)2NiMnO6 thin films are found to display longrange B-site order and the Ni2+/Mn4+ electronic configuration, which is the required
condition for a long-range ferromagnetism. Indeed, ferromagnetic behaviour is recorded
but with a reduced Curie temperature probably due to the epitaxial strain of the
substrate. Instead, BiMnO3 thin films are found to exhibit similar Curie temperature to
that of bulk specimens, but with a reduced saturated magnetisation which is ascribed to
slightly off-stoichiometric samples driven by the presence of Bi vacancies and the
subsequent formation of small amounts of Mn4+ replacing Mn3+ cations. Remarkably
enough for the implementation of these films in future multilayer structures devices in
which flat surfaces is a requirement, two-dimensional growth mode is obtained for
(Bi0.9La0.1)2NiMnO6 thin films, attaining very low rough surface (between one and two
unit cells), whereas BiMnO3 thin films were in all cases displaying a clear threedimensional growth mode, yielding rougher surface morphology.
Finally, in order to study the dielectric/resistive, magnetoelectric and ferroelectric
properties parallel-plate capacitors were fabricated using single-crystal (001)-oriented
iii
Nb doped SrTiO3 substrates as bottom electrode and sputtered Pt as top electrodes. First
part of the electric measurements is devoted to the ferroelectric properties. In
(Bi0.9La0.1)2NiMnO6 thin films ferroelectric domains switching current is measured,
which allows conclusively stating that (Bi,La)2NiMnO6 compounds are indeed
ferroelectric up to at least 10% La content. By structural characterisation the
ferroelectric transition temperature is inferred to be around 450 K, well above room
temperature. Instead, BiMnO3 thin films were not able to be proved its possible
ferroelectric character (which is still on debate in the scientific community), probably
due to the fact that leakage was too large with regard to the ferroelectric domain
switching current that may masked any footprint of ferroelectricity by conventional
macroscopic measurements. The second part of this bloc is devoted to study the
dielectric properties and the possible magnetoelectric coupling of these compounds. It is
worth remarking that in this work both the dielectric response and the magnetoelectric
response was assessed by impedance spectroscopy, the latter using magnetic fields
while recording the impedance response, with the final aim of observing any deviation
of the dielectric permittivity of these compounds either in the vicinity of the
ferromagnetic transition temperature or when applying a magnetic field. Either
phenomenon would indicate that the ferroelectric and ferromagnetic orders display a
certain degree of coupling. Nonetheless, special attention is given to the conventional
artefacts these measurements often produce when performed on dielectric thin films,
causing misleading interpretations, like apparent colossal dielectric constants and/or
apparent large magnetoelectric couplings. For this aim a thorough study is devoted, in
which simulations of real dielectric materials are carried out covering the different
sources of artefacts in order to better understand the dielectric and magnetoelectric data.
Following these precautions the intrinsic dielectric and magnetoelectric response of
BiMnO3 and (Bi0.9La0.1)2NiMnO6 thin films are extracted. Despite the fact that BiMnO3
dielectric data shows clear magnetoelectric signs, results points to a weak
magnetoelectric coupling, which is especially emphasised in (Bi0.9La0.1)2NiMnO6 thin
films, probably driven by the fact that magnetism and ferroelectricity arise by two
independent mechanisms in these Bi-based compounds.
iv
Resumen
Los materiales multiferroicos, en los cuales coexisten en la misma fase un
ordenamiento ferroeléctrico y magnético, han recibido mucho interés en los últimos
años. La posibilidad de que estén acoplados los dos órdenes ferroicos permite nuevas
funcionalidades en estos materiales como el control eléctrico de la magnetización o, por
el contrario, el control magnético de la polarización. La realización de dicho
acoplamiento magnetoeléctrico no solo sería interesante en términos de investigación
básica, sino que abriría camino para el diseño de nuevas aplicaciones magnetoeléctricas,
especialmente en el campo de la spintrónica, como filtros de spin o uniones túneles
magnéticas controladas mediante campos eléctricos en lugar de campos magnéticos y
por lo tanto promoviendo una nueva generación de dispositivos de almacenamiento de
alta densidad y bajo consumo. Para este último propósito, los multiferroicos que poseen
un
ordenamiento
ferromagnético
tendrían
mayores
ventajas
que
aquellos
antiferromagnéticos debido a que los primeros mostrarían magnetización neta y por lo
tanto permitirían un control más fácil del estado magnético. No obstante, es el orden
antiferromagnético el que prevalece en estos materiales. Por eso es necesario la
búsqueda de nuevos materiales que sean ferromagnéticos y ferroeléctricos.
Los óxidos en estructura perovskita y doble perovskita basados en Bi, BiBO3 y
Bi2BB’O6, respectivamente, donde B y B’ son iones magnéticos de metales de
transición (es decir, con la capa electrónica externa d parcialmente ocupada), presentan
un excelente punto de partida para investigar nuevos materiales ferromagnéticos y
ferroeléctricos. En estos compuestos la ferroelectricidad se origina debido a la actividad
estereoquímica de los cationes Bi3+. La capa externa electrónica de los orbitales 6s de
dichos iones, llamados lone pairs, no participan en los enlaces químicos, por lo que
rodeados por los aniones oxígeno en la perovskita se desplazan del centro de simetría
formando un dipolo eléctrico y rompiendo la simetría de inversión espacial (condición
necesaria, aunque no suficiente, para que se produzca el ordenamiento ferroeléctrico).
Por el contrario, el magnetismo en estos compuestos se produce como consecuencia de
la interacción de supercanje entre los iones magnéticos, es decir, los cationes B, por
medio de los iones de oxígenos adyacentes (B – O – B). Dependiendo en gran medida
de la configuración electrónica de los orbitales d de los cationes B, los cuales en
v
perovskitas se dividen en orbitales de alta energía eg y baja energía t2g, dicha interacción
de supercanje es ferromagnética o antiferromagnética. En perovskitas ideales en las
cuales el ángulo de enlace químico B – O – B es 180º, tanto la configuración B
(orbitales eg vacíos) – O – B (orbitales eg vacíos) como B (orbitales eg semillenos) – O –
B (orbitales eg semillenos) dan lugar a interacciones antiferromagnéticas, mientras que
B (orbitales eg semillenos) – O – B (orbitales eg vacíos) dan lugar a interacciones
ferromagnéticas. Debido a que el sitio B es ocupado por un solo tipo de ion en
perovskitas y, en general, con el mismo estado de oxidación, lo que implica el mismo
llenado de los orbitales eg, las interacciones antiferromagnéticas son mucho más
comunes que las ferromagnéticas. En cambio, eligiendo apropiadamente los cationes B
y B’ en doble perovskitas, se puede diseñar que las interacciones de supercanje sean
ferromagnéticas. Es por eso que los óxidos en estructura de doble-perovskita basados en
Bi pueden proporcionar la posibilidad de ingeniar ferromagnetismo de largo alcance
(siempre que se produzca un ordenamiento cationico B de largo alcance siguiendo
cadenas de B – B’ – B – B’ – … ) y por consiguiente superar la escasez de
multiferroicos ferromagnéticos.
En concreto, los sistemas BiMnO3 y Bi2NiMnO6 son los únicos de la familia de
óxidos en estructura perovskita basados en Bi que hasta la fecha han manifestado un
ordenamiento ferromagnético en su forma masiva, con temperaturas de Curie alrededor
de 105 K y 140 K, respectivamente. Por otro lado, son candidatos prometedores de
manifestar
ordenamiento
ferroeléctrico
debido
a
la
mencionada
actividad
estereoquímica de los cationes de Bi3+, por lo que ambos sistemas son investigados, en
láminas delgadas, en el trabajo de esta tesis.
En primer lugar, esta tesis aborda el problema de sintetizar estos compuestos. En
este proceso se topó con tres principales obstáculos. Primero, estos compuestos basados
en Bi son altamente metaestables, lo que implica que en su forma masiva sólo se pueden
sintetizar bajo condiciones extremas: altas temperaturas y altas presiones (del orden de
los GPa). La estrategia que se usó para eludir las altas presiones consistió en reemplazar
la presión mecánica por el estrés epitaxial, es decir, usando sustratos cuyos parámetros
de red cristalinos fueran semejantes a los del compuesto que se tiene que formar. Para
este propósito, estos compuestos basados en Bi se crecieron sobre sustratos
monocristalinos de SrTiO3 orientados (001) por ablación de láser pulsado (PLD).
vi
Segundo, Bi es un elemento altamente volátil y por consiguiente la temperatura de
síntesis de estos compuestos no fue un parámetro de crecimiento libre. Esto llevó al uso
de bajas temperaturas de crecimiento con el objeto de impedir el crecimiento de láminas
delgadas no estequiométricas o incluso la no formación del compuesto cuando la
deficiencia en Bi fuera demasiado grande. No obstante, el carácter metaestable de estos
compuestos demandaba el uso de altas temperaturas en el proceso de síntesis. Para
equilibrar estos dos requerimientos antagónicos se usó blancos de PLD enriquecidos en
Bi en el caso de BiMnO3 y una sustitución parcial (10 %) de Bi3+ por cationes La3+ en el
caso de Bi2NiMnO6. El dopaje con La da lugar a un volumen ligeramente reducido de la
celda unidad, ejerciendo la presión química (equivalente a una presión hidrostática) que
contribuye a prevenir la desabsorción de Bi durante el proceso de crecimiento. Tercero,
tanto en el sistema ternario Bi – Mn – O como cuaternario Bi – Ni – Mn – O se
encontró una fuerte tendencia multifásica, especialmente en el primero, en los cuales,
aparte de los compuestos deseados BiMnO3 y Bi2NiMnO6, se forman diferentes fases
parásitas de óxidos como Mn3O4, Bi2O3 y MnO2 en el primer caso y NiO en el segundo.
Como consecuencia de todos estos factores la estabilización monofásica de tanto
BiMnO3 como (Bi0.9La0.1)2NiMnO6 fue dificultada en gran medida y solo se pudo
conseguir bajo una ventana estrecha de condiciones de crecimiento. Especialmente
crítico fue la temperatura de depósito, la cual sólo permitía una ventana de 10ºC
alrededor de 630ºC y 620ºC para la síntesis de BiMnO3 y (Bi0.9La0.1)2NiMnO6,
respectivamente.
Una vez controladas las condiciones de crecimiento para la estabilización
monofásica de los compuestos de Bi, la caracterización estructural evidenció que tanto
BiMnO3 como (Bi0.9La0.1)2NiMnO6 crecen completamente coherentes (tensionadas por
compresión y por tracción, respectivamente) sobre los sustratos SrTiO3, por lo tanto
adaptando el parámetro de red en el plano al del sustrato cúbico y por consiguiente
adoptando una estructura tetragonal. Suficientemente importante para las propiedades
magnéticas, las láminas delgadas de (Bi0.9La0.1)2NiMnO6 manifiestan ordenamiento
catiónico de largo alcance en el sitio B y la configuración electrónica Ni2+/Mn4+. De
hecho, su comportamiento ferromagnético es corroborado, aunque con una temperatura
de Curie reducida con respecto a su forma masiva probablemente debida al estrés
epitaxial del sustrato. En cambio, en las láminas delgadas de BiMnO3 se encontró que
exhibían temperaturas de Curie similares a las halladas en especímenes en forma
vii
masiva, aunque con una reducida magnetización de saturación la cual se atribuye a una
ligera desviación estequimétrica de las muestras por la presencia de vacantes de Bi y la
subsiguiente formación de pequeñas cantidades de Mn4+ remplazando los cationes
Mn3+. Un aspecto importante a la hora de implementar estas láminas delgadas en
dispositivos de estructura multicapa es el requerimiento de superficies planas. En el
caso de las láminas delgadas de (Bi0.9La0.1)2NiMnO6 se obtuvo un crecimiento
bidimensional, logrando superficies con muy baja rugosidad (entre una y dos celdas
unidades). Sin embargo, las láminas delgadas de BiMnO3 mostraron un crecimiento
tridimensional en todos los casos, dando lugar a una morfología superficial más rugosa.
Finalmente, con el objeto de estudiar las propiedades dieléctricas/resistivas,
magnetoeléctricas y ferroeléctricas condensadores con geometría de electrodos planoparalelos fueron fabricados, usando sustratos monocristalinos de SrTiO3 dopados con
Nb como electrodo inferior y Pt depositado por pulverización catódica como electrodos
superiores. La primera parte de las medidas eléctricas se centra en las propiedades
ferroeléctricas. En las láminas delgadas de (Bi0.9La0.1)2NiMnO6 se consiguió medir
corriente eléctrica que era debida únicamente al cambio de orientación de los dominios
ferroeléctricos, lo cual permitió afirmar de forma concluyente que los compuestos
(Bi,La)2NiMnO6 son ferroeléctricos, al menos hasta un 10% de contenido de La. Por
medio de caracterización estructural, se deduce que la temperatura de transición
ferroeléctrica es aproximadamente sobre los 450 K, por encima de temperatura
ambiente. En cambio, no fue posible revelar el posible carácter ferroeléctrico de
BiMnO3 (el cual es todavía materia de debate en la comunidad científica),
probablemente debido a que las pérdidas eléctricas eran demasiado grandes
enmascarando cualquier posible huella de ferroelectricidad por medio de medidas
convencionales macroscópicas. La segunda parte de este bloque se centra en el estudio
de las propiedades dieléctricas y el posible acoplamiento magnetoeléctrico de dichos
compuestos. Vale la pena remarcar que en este trabajo tanto la respuesta dieléctrica
como magnetoeléctrica se ha evaluado por medio de la técnica de espectroscopia de
impedancias, usando además campos magnéticos en el último caso, con el objeto final
de observar cualquier variación de la permitividad dieléctrica de estos compuestos tanto
en las cercanías de la temperatura de transición magnética como debido a la aplicación
de campo magnético. Ambos fenómenos indicarían un acoplamiento entre los órdenes
ferroeléctrico y ferromagnético. Se da una especial atención a los artefactos
viii
convencionales que producenc frecuentemente este tipo de medidas eléctricas, llevando
a interpretación errónea de los resultados como constantes dieléctricas aparentemente
colosales o acoplamientos magnetoeléctricos aparentemente fuertes. Con este propósito
un exhaustivo estudio es presentado en la tesis, en el cual se llevan a cabo simulaciones
del comportamiento de materiales dieléctricos reales cubriendo las diferentes fuentes de
artefactos con el objeto de entender mejor los datos medidos sobre la respuesta
dieléctrica y magnetoeléctrica. Siguiendo estas precauciones, se extraen las propiedades
dieléctricas y magnetoeléctricas intrínsecas de BiMnO3 y (Bi0.9La0.1)2NiMnO6. A pesar
de que los resultados de las medidas dieléctricas de BiMnO3 muestran claros signos de
acoplamiento magnetoeléctrico, dicho acoplamiento es débil, especialmente enfatizado
en (Bi0.9La0.1)2NiMnO6, probablemente debido al hecho de que en los compuestos
basados en Bi el magnetismo y la ferroelectricidad se originan por medio de dos
mecanismos independientes.
ix
x
Contents
1. Introduction .............................................................................................. 1
1.1 Multiferroics ......................................................................................... 3
1.1.1 Ferroic properties ...................................................................... 3
1.1.2 Motivation ................................................................................ 5
1.1.3 Magnetoelectric coupling .......................................................... 6
1.1.4 Pathways to the coexistence of magnetism
and ferroelectricity .................................................................... 9
1.2 Bi-based multiferroic perovskites.......................................................... 11
1.2.1 Perovskite structure ................................................................... 12
1.2.2 Ferroelectricity in Bi-containing perovskite oxides:
the role of the lone-pair electrons .............................................. 13
1.2.3 Magnetic order in Bi-containing perovskite oxides .................... 14
1.2.4 The BiMnO3 system .................................................................. 18
1.2.5 The Bi2NiMnO6 system............................................................. 22
1.2.6 La-doping in Bi2NiMnO6 system............................................... 26
1.2.7 State-of-the-art of Bi-based multiferroic perovskite oxides ........ 28
1.3 Epitaxial engineering ............................................................................ 33
1.3.1 Stabilisation of metastable oxides .............................................. 34
1.3.2 Epitaxial tuning ......................................................................... 34
1.4 Outline of the thesis .............................................................................. 36
2. Experimental techniques and data analysis ............................................ 43
2.1 Growth techniques ................................................................................ 45
2.1.1 Pulsed laser deposition......................................................... 45
2.1.2 Thin film growth process ..................................................... 46
2.1.3 Target fabrication ................................................................ 48
2.2 Structural characterisation techniques ................................................... 49
2.2.1 X-ray Diffraction ................................................................. 49
2.2.2 X-ray Reflectivity ................................................................ 58
2.2.3 Transmission electron microscopy ....................................... 60
2.2.4 X-ray Diffraction using Synchrotron radiation ..................... 63
2.3 Surface topography characterisation techniques .................................... 64
2.3.1 Field emission scanning electron microscopy....................... 64
xi
2.3.2 Atomic force microscopy ..................................................... 66
2.4 Composition characterisation techniques............................................... 67
2.4.1 X-ray photoelectron spectroscopy ........................................ 67
2.4.2 Variable-voltage electron microprobe analysis ..................... 69
2.4.3 Electron energy loss spectroscopy........................................ 71
2.5 Functional characterisation techniques .................................................. 72
2.5.1 Magnetic characterisation .................................................... 72
2.5.2 Electric characterisation ....................................................... 73
2.5.3 Ferroelectric characterisation ............................................... 74
3. Electric measurements ............................................................................. 77
3.1 Parallel-plate capacitors fabrication ...................................................... 79
3.2 Dielectric and resistive measurements of dielectric thin films ............... 81
3.2.1 Impedance spectroscopy............................................................ 81
3.2.2 Complex dielectric constant and ac conductivity ....................... 86
3.2.3 Extrinsic contributions to the dielectric measurements............... 89
3.2.4 Magnetocapacitance measurements ........................................... 95
3.3 Ferroelectric hysteresis measurements .................................................. 97
4. BiMnO3 thin films .................................................................................... 105
4.1 Single-phase stabilisation...................................................................... 107
4.1.1 Dependence on temperature ...................................................... 108
4.1.2 Dependence on oxygen pressure................................................ 112
4.1.3 Dependence on thickness .......................................................... 115
4.2 Structural characterisation and surface topography ............................... 119
4.2.1 Texture of the film .................................................................... 119
4.2.2 Reciprocal space maps and lattice parameters............................ 122
4.2.3 Surface topography ................................................................... 128
4.3 Magnetic characterisation of Bi – Mn – O films .................................... 130
4.4 Electric and magnetoelectric properties ................................................. 134
4.4.1 Background ............................................................................... 134
4.4.2 Complex dielectric constant and ac conductivity.
Qualitative analysis ................................................................... 135
4.4.3 Impedance spectroscopy. Quantitative analysis ......................... 138
4.4.4 Magnetoelectric response .......................................................... 148
xii
4.5 Ferroelectric properties ......................................................................... 151
5. (Bi0.9La0.1)2NiMnO6 thin films .................................................................. 155
5.1 Single-phase stabilisation...................................................................... 157
5.1.1 Dependence on temperature ...................................................... 158
5.1.2 Dependence on oxygen pressure................................................ 160
5.1.3 Dependence on thickness .......................................................... 162
5.2 Structural characterisation and surface topography ............................... 164
5.2.1 Texture of the film .................................................................... 164
5.2.2 Reciprocal space maps and lattice parameters............................ 167
5.2.3 Microstructure characterisation
by transmission electron microscopy ......................................... 174
5.2.4 B-site order ............................................................................... 177
5.2.5 Surface topography ................................................................... 183
5.3 Chemical analysis ................................................................................. 185
5.3.1 Composition analysis ................................................................ 185
5.3.2 Oxidation state of B-cations ...................................................... 187
5.4 Magnetic characterisation ..................................................................... 191
5.5 Ferroelectric characterisation ................................................................ 196
5.5.1 Background ............................................................................... 196
5.5.2 Electric characterisation of the ferroelectric properties .............. 197
5.5.3 Ferroelectric phase transition..................................................... 202
5.6 Electric and magnetoelectric properties ................................................. 208
5.6.1 Background ............................................................................... 208
5.6.2 Complex dielectric constant and ac conductivity.
Qualitative analysis ................................................................... 210
5.6.3 Impedance spectroscopy. Quantitative analysis ......................... 214
5.6.4 Magnetoelectric response .......................................................... 223
Appendix A: Lattice parameters from XRD data ....................................... 231
Appendix B: Diamagnetism of SrTiO3 substrates ...................................... 235
Appendix C: Capacitances values from the R-CPE element ...................... 237
List of publications ....................................................................................... 239
List of oral presentations ............................................................................. 241
xiii
xiv
Chapter 1. Introduction
Chapter 1
Introduction
1
Chapter 1. Introduction
2
Chapter 1. Introduction
1.1 Multiferroics
1.1.1 Ferroic properties
Multiferroics are materials where at least two ferroic orders coexist in the same
phase. The definition of the term ferroic aimed to characterise materials in which
domains are formed, having a corresponding net macroscopic magnitude that can be
hysteretically switched by applying an external field, i.e. ferroelectric, ferromagnetic,
ferroelastic and ferrotoroidic orders (primary ferroics) [1, 2], see table 1.1. Nonetheless,
antiferroic orders, which basically consist of antiferromagnetism –i.e. also
ferrimagnetism– and antiferroelectricity, are widely accepted to be also included in the
extended definition of the term multiferroic, as listed in Table 1.1.
Fig. 1.1 – Illustrative sketch of the primary (solid lines) and cross-coupling (dashed
lines) interactions allowed in multiferroic materials. P, M, ε and T denote the primary
ferroic orders, namely polarisation, magnetisation, strain and ferrotoroidic order,
respectively; whereas E, H, σ and E x H denote their conjugate fields, namely electric
field, magnetic field, stress and cross electric-magnetic field, respectively. Adapted from
Ref. [3].
3
Chapter 1. Introduction
Ferroic property
Description
Ferroelectric order
Antiferroelectric
order
Ferromagnetic order
Materials that below a certain temperature undergo a phase
transition in which an ordering of dielectric dipole moments
is present, leading to spontaneous polarization (P) that can
be hysterically switched by applying an external electric
field (E).
Materials that below a certain temperature undergo a phase
transition in which an antiparallel ordering of dielectric
dipole moments is present, leading to zero overall
polarisation.
Materials that below a certain temperature undergo a phase
transition in which an ordering of magnetic moments is
present, leading to spontaneous magnetisation (M) that can
be hysterically switched by applying an external magnetic
field (H).
Antiferromagnetic
order
Materials that below a certain temperature undergo a phase
transition in which an antiparallel ordering of magnetic
moments is present, leading to zero overall magnetisation.
Ferrimagnetic order
Materials that below a certain temperature undergo a phase
transition in which an antiparallel ordering of magnetic
moments is present, but the opposing magnetic moments
are unequal, leading to a remaining net magnetisation (M)
that can be switched hysterically by applying a magnetic
field (H).
Ferroelasticity
Materials that below a certain temperature possess
spontaneous strain (ε), which can be hysterically switched
by applying an external stress (σ).
Ferrotoroidic order
Materials that below a certain temperature an ordering of
the so-called toroidal moments, T ∝ ∑n rn × Sn, is present,
where rn denotes the radius vector (from an origin of
coordinates) and Sn the spin of the n magnetic ion. These
toroidal moment should be hysterically switched by crossed
electric and magnetic field.
Table 1.1 – Description of the ferroic orders
The coexistence of different ferroic orders leads to additional interactions in
multiferroic materials, as illustrated in Fig. 1.1. Whereas in conventional ferroic
materials, its ferroic order is modified by its conjugate field (i.e. the magnetic field
modifies the magnetisation, the electric field the polarisation, etc), in multiferroic
4
Chapter 1. Introduction
materials exists the possibility that two or more ferroic orders are coupled, which would
allow cross-interactions between the ferroic properties and their conjugated fields, i.e.
tuning the magnetisation by an electric field, tuning the strain by a magnetic field and so
on (Fig. 1.1).
Among all kinds of multiferroics, those showing both ferroelectric and magnetic
order draw special attention in terms of magnetoelectric properties, as will discussed
later on, on which this work is focused. Thus, for the sake of simplicity, on the
following the term multiferroicity will be used to refer, exclusively, to those materials
being ferroelectric and magnetic (either ferromagnetic or antiferromagnetic).
1.1.2 Motivation
In terms of fundamental research, multiferroic materials are very appealing just by
the mere fact of combining ferroelectric and magnetic order. Whereas electricity and
magnetism were demonstrated to be unified in the common discipline of
electromagnetism during 19th century, culminated by Maxwell’s equations which
specify how magnetic and electric fields relate to each other, ferroelectricity and
magnetism in matter tend to be independent disciplines and rarely found together.
Indeed, microscopically both ferroic orders arise from different origin: electric dipole
ordering versus spin ordering. Thus, the research on new multiferroic materials will
contribute to make advances in the comprehension of the mechanism which enable
multiferroicity to exist and how both orders may relate to each other.
From the technological point of view, magnetic and ferroelectric materials are
widely used in many devices. The former have played an important role in the stored
data devices (hard disks, magnetic RAM’s, ...) as well as sensors, read heads, .... The
latter are used in sensors and transducers because of their large piezoelectric response,
in capacitors because of their high dielectric permittivity and also in storage data
devices (ferroelectric RAM’s). Thus, multiferroics are especially interesting not only
because they have the same properties, and therefore the same applications, as their
‘parents’ (ferroelectrics and magnetics) have, but also because of the interplay between
magnetism and ferroelectricity, which gives an extra degree of freedom and hence
additional funcionalities.
5
Chapter 1. Introduction
Some of these additional applications could be the four-state memories, in which
the ferroelectric and ferromagnetic character of the multiferroic is used to encode the
information in either four resistive states [4 – 6] (also proposed eight resistive states
[7]), or the electric control of magnetic RAM’s [6, 8]—if the magnetoelectric coupling
is large enough (see Sect. 1.1.3)—, which would reduce, to a large extent, the inherent
problem of the crosstalk (as the electric field can be applied very localized) and energy
consumption (as sustaining and producing magnetic fields are much more energetically
inefficient than electric fields), allowing, thus, high density and low-energy consuming
magnetic RAM’s.
Moreover, electrically controlled magnetic sensors, electrically tuneable microwave
applications, such as filters, oscillators and phase shifters, and other kinds of
applications in magnetoelectronics and spintronics have also been proposed for
multiferroic materials [6, 8 – 12], and, possibly, new ones are expected to be suggested
in future.
1.1.3 Magnetoelectric coupling
The magnetoelectric coupling or magnetoelectric effect describes any effect on the
polarisation by applying a magnetic field, H, or, conversely, any effect on the
magnetisation by applying an electric field, E. By the Neumann principle [13], which
states that the symmetry elements of all the physic properties of a material should be
contained in the symmetry elements of its crystalline structure, magnetoelectric
coupling is enabled in multiferroic materials.
This magnetoelectric coupling can be described thermodynamically. In terms of the
expansion of the free energy, F, of a magnetoelectric media, i.e. F = F ( H , E ) , it follows
[14]:
1
1
F ( H , E ) = F0 − Pi s Ei − M is H i − ε 0 χ ije Ei E j − χ ijm H i H j − α ij Ei H j − ...
2
2
6
(1.1)
Chapter 1. Introduction
where, as listed in table 1.2, Pi s and M is denote the spontaneous polarisation and
magnetisation, respectively; χije and χijm are the electric and magnetic susceptibility,
respectively ; and α ij is the linear magnetoelectric coupling, which entails the induction
of polarisation and magnetisation by a magnetic and electric field, respectively, what is
called the linear magnetoelectric effect. Note that the expansion 1.1 has been cut in the
first order magnetoelectric term. There are also quadratic magnetoelectric terms, and so
on, but in general they are much weaker than the linear magnetoelectric effect [14].
Corresponding
mechanism
Spontaneous moment
Induced moment
linear magnetoelectric
coupling
Contribution to
polarisation
Pi s
1
ε 0 χ ije Ei
2
Contribution to
magnetisation
M is
1 m
χ ij H i
2
α ij H j
α ij Ei
Table 1.2 – Significance of the expansion terms of the free energy
Hence, the polarisation and the magnetisation can be expressed as [14]:
∂F
= Pi s + ε 0 χ ije E j + α ij H j + ...
Pi ( H , E ) = −
∂Ei
∂F
= M is + χ ijm H j + α ij E j + ...
M i (H , E) = −
∂H i
(1.2)
The magnetoelectric coefficient is, though, subjected to the magnetic and electric
susceptibilities, which determine the upper bound on the magnitude of the
magnetoelectric effect [15]:
αij2 < χiie χ mjj
(1.3)
Therefore, as ferromagnetic and ferroelectric materials show large magnetic and
electric susceptibilities, respectively, multiferroic materials are enabled to show large
magnetoelectric coupling. On the other hand, as the magnetic (and electric)
susceptibility tend to diverge around the transition temperatures, the magnetoelectric
coupling is expected to be larger around the Curie temperatures. Yet it is worth
7
Chapter 1. Introduction
mentioning that the sole coexistence of the two ferroic orders is not a sufficient
condition for magnetoelectric coupling to occur, which is a more restrictive property.
On the other hand, when the magnetic and ferroelectric parameter are coupled to
each other, the magnetic order is coupled to the polarisation and consequently to the
dielectric permittivity. The origin of which can also be understood in the framework of
the Ginzburg-Landau theory [16]. In the simplest scenario, the Taylor expansion of the
free energy, F, now as a function of the magnetisation, M, and polarisation, P, in a
magnetoelectric media, follows:
F ( M , P ) = F0 +
a 2 b 4
a'
b'
M + M + ... + P 2 + P 4 + ... + γ M 2 P 2 + ...
2
4
2
4
(1.4)
where no odd terms appear following the symmetry restrictions F(M) = F(-M) and F(P)
= F(-P) as both states are energetically equivalent. The coefficients a, a’, b, b’ and γ are
in general temperature dependent. The γM2P2 is hence the first order term allowed in the
Taylor expansion related to the magnetoelectric coupling.
When applying an external electric, E, and magnetic, H, field, which couples
linearly with the polarisation and magnetisation, respectively, expression 1.4 should be
rewritten:
F ( M , P ) = F0 − HM +
a 2 b 4
a'
b'
M + M + ... − EP + P 2 + P 4 + ... + γ M 2 P 2 + ...
2
4
2
4
(1.5)
The electric susceptibility can be computed by ( χ e )−1 ∼
∂f 2
∼ a '+ 3b ' P 2 + γ M 2 [16].
∂P 2
Hence, in a magnetoelectric material the dielectric permittivity is not only modified by
the polarisation but also by the square of magnetisation (as long as γ ≠ 0) [16].
Therefore, a useful, and widely extended [16 – 19], indirect way to bear out the
occurrence of the coupling of the two ferroic orders consists of looking for deviations of
the dielectric permittivity either in the vicinity of the magnetic transition temperature
8
Chapter 1. Introduction
and/or when applied a magnetic field, the so-called magnetocapacitance or
magnetodielectric effect.
1.1.4 Pathways to the coexistence
magnetism and ferroelectricity
of
Despite the large number of ferroelectric or magnetic materials existing in nature,
the combination of both ferroic orders in one intrinsic material seems to be quite elusive
to be encountered. The reasons for this scarcity of multiferroic materials can be
summarised in the following [10, 11, 20]:
1) Whereas magnetic materials can be either insulating or conductive, ferroelectric
materials can solely be insulating, otherwise an applied electric field would
induce an electric current rather than switching ferroelectric domains. This
restricts the search for multiferroic materials to those magnetic materials that are
insulators.
Fig. 1.2 – (a) Ferroelectric material (BaTiO3) under spatial inversion symmetry:
changes orientation of electric dipole moment, D. (b) Classical representation of a
particle with spin angular momentum I under time reversal operation.
9
Chapter 1. Introduction
2) Second, from crystal symmetry considerations (see Fig. 1.2) ferroelectricity
breaks the spatial inversion symmetry, which requires non-centrosymmetric
crystal structures for ferroelectric order to occur [2]. Moreover, it should
accomplish additional criteria: ferroelectric order can only be enabled in polar
point groups. This leaves 10 out of the 32 possible point groups (or crystal
classes) that can sustain spontaneous polarisation [13, 21]. Conversely,
magnetism breaks time-reversal symmetry [2] (see Fig. 1.2). When time
reversal operation is included in the set of the customary symmetry operations
(rotations and reflexions) contained in the 32 point groups, 90 additional point
groups should be included, in total leading to 122 magnetic point groups (or
Shubnikov point groups) [13, 21]. Combination of the two symmetry
restrictions which multiferroics must fulfil leaves only 21 magnetic point groups
(out of 122) that enable ferroelectric and magnetic orders to coexist in the same
phase [10, 11, 20, 21]. Moreover, if we restrict the magnetic materials to those
allowed
displaying
spontaneous
magnetisation
(i.e.
excluding
antiferromagnetics) the list of possible multiferroic candidates is then reduced to
13 magnetic point groups [10, 11, 20, 21].
3) Since most of ferroelectric and a large number of magnetic materials are
transition metal oxides with the ABO3 perovskite structure, see Sect. 1.2.1, (e.g.
BaTiO3 and (La,Sr)MnO3), much of the attention was reasonably drawn to this
structure for the search for multiferroic materials. Both, in the ferroelectric and
magnetic perovskites it is usually the B cation which drives the ferroelectric
displacement and the magnetic order, respectively. In the case of ferroelectrics,
the B cation displaces from the centre of the surrounding oxygen octaheadra,
breaking the centrosymmetry and creating an electric dipole [Fig. 1.2 (a)]. Yet
this condition requires the B cation to have a d0 electron configuration, i.e.
empty d orbitals like Ti4+, to minimize the Coulombian electrostatic repulsion of
the surrounding oxygen anions [20]. Magnetism in transition metal perovskites
arises from magnetic superexchange interactions, see Sect. 1.2.3, (or double
exchange for conductive magnetic oxides) of the B cations mediated by the
adjacent oxygen ions [20, 22]. Yet this condition requires B cation to possess a
magnetic moment, which is only possible when the d orbitals of the B cation are
10
Chapter 1. Introduction
partially occupied. Thus, there is an inherent mutual exclusion between
ferroelectricity and magnetism in perovskites oxides [19].
To date, most of the attempts to design multiferroic materials have been based on
looking for new mechanisms of ferroelectricity, while maintaining the same recipes for
magnetism. Depending on these mechanisms, multiferroics have been classified into
two types, as described by Khomskii [23]: In Type-I multiferroics ferroelectricity and
magnetism rely on two independent mechanisms, whereas in Type-II ferroelectricity
arises from the magnetic order, i.e. ferroelectricity exists only in a magnetically ordered
state. The latter is expected to produce large magnetoelectric coupling as one order is
intrinsically related to the other, but such ferroic orders tend to appear only at rather low
temperatures. The most studied example of Type-II multiferroics is the Rare-Earth
manganites, in which ferroelectricity appears because of the particular spiral or cycloid
arrangement of the spins of Mn cations [24]. Contrarily, Type-I multiferroics tend to
show much higher ferroic transition temperatures at the expense of small
magnetoelectric coupling. To this group belong the multiferroics in which the
ferroelectric order might be achieved (though not demonstrated in all cases) as a
consequence of (i) a particular charge ordering, like (Pr,Ca)MnO3 [25], (ii) tilting of the
BO6 octahedron, the so-called geometrical ferroelectrics, like YMnO3 [26], and (iii) of
the stereochemical activity of the lone pairs of Bi3+ and Pb2+ cations, located at the Asite in the perovskite, like BiFeO3 [27]. This latter approach applies to the systems
studied here.
1.2 Bi-based multiferroic
perovskites
The simplest scenario where both ferroic orders are to be independently achieved in
transition metal perovskite oxides would naturally lead to use one of the cations for
inducing the ferroelectric order, while using the other one for the magnetism. One
possibility is the exploitation of a d0 transition metal cation located on the B-site and a
magnetic cation on the A-site, for example in EuTiO3 [28]. The second possibility is the
use of stereochemical active cations like Bi3+ or Pb2+ at the perovskite A-site inducing
11
Chapter 1. Introduction
ferroelectricity due to lone-pair electrons, and a magnetic cation located on the B-site,
as described in this section.
1.2.1
Perovskite structure
The perovskite structure, whose chemical formula is given by ABO3 (where A and B
are cations), is formed by the alternation of BO2 and AO atomic planes along any of the
orthogonal directions iˆ, ˆj , kˆ , as shown in Fig. 1.3, in its ideal cubic configuration. As a
result of these staggered atomic planes, B cations are surrounded by 6 first-neighbour
oxygen anions, forming the characteristic BO6 octahedron, whereas A cations are
surrounded by 12 oxygen anions (Fig. 1.3).
Fig. 1.3 – Ideal perovskite structure, ABO3.
The stability of this structure is determined by the Goldschmidt tolerance factor,
which is defined as follows:
t=
rA + rO
2 ⋅ ( rB + rO )
(1.6)
where rA, rB and rO denote the ionic radii of A, B cations and oxygen anion, respectively.
The ideal cubic perovskite, such as the one shown in Fig. 1.3, is found when t = 1.
Lower values of t means that the ionic radius of the A cation is smaller than that of the B
12
Chapter 1. Introduction
cation, so that, in order to achieve a close packaging of the ions, BO6 octahedrons tilt
(Fig. 1.4), forming, typically, orthorhombic or rhombohedral structures. Instead, when t
> 1 the size of the A cation is too large to be accommodated in the cubic perovskite and
different hexagonal polymorphs become stable (Fig. 1.4).
Fig. 1.4 – Stability of the perovskite structures as a function of the tolerance factor, t.
1.2.2
Ferroelectricity
of
Bi-containing
perovskite oxides: the role of the lone pair
electrons
An alternative route to the d0 transition metal ion, located at the B-site, as the
mechanism for the ferroelectric instability, is the use of stereochemical active ions like
Bi3+ or Pb2+, which always locate at the A-site. The electronic configuration of Bi3+ (and
also Pb2+), [Xe]4f145d106s26p0, signals empty p-states as the lowest unoccupied state,
which form a covalent bond with the surrounding oxygen. Instead, the two outer
electrons of the 6s orbitals, called lone pairs, do not participate in chemical bonds. In
absence of interactions the lone pairs are nearly spherically distributed, but when
surrounded by the oxygen anions they shift away from the centrosymmetric position
due to the Coulombian electrostatic repulsion, forming a localized lobe-like distribution
(very much alike the ammonia molecule [Fig. 1.5]) [29]. Thus, the lone pairs, which
form an electric dipole, break the spatial inversion symmetry and become the driving
force for the ferroelectric distortion in all Bi-based multiferroics.
13
Chapter 1. Introduction
Fig. 1.5 – (a) Schematic representation of the lobe-like distribution of the 6s2 lone-pair
electrons in Bi-based perovskite structures, BiBO3, breaking the spatial inversion
symmetry. (b) Lone-pair 2s2 in the ammonia molecule.
Still, it is worth mentioning that the non-centrosymmetric structure is a requirement
for ferroelectricity to be enabled, but not a sufficient condition, as cooperative
behaviour between the electric dipoles and hysteretically electric-field switching of the
polarisation of the formed ferroelectric domains is to be additionally accomplished.
In an ideal perovskite the electrostatic repulsion of the oxygen anions over the lone
pair electrons of Bi3+ cations is softened along the [111] pseudocubic direction, which,
thus, tend to be the polar axis in Bi-multiferroic perovskites. Yet the common distortion
of the ideal cubic perovskite in these compounds and/or the epitaxial strain in thin films
(as will discussed in Sect. 1.3) may severely modify this polar orientation.
1.2.3 Magnetic order
perovskite oxides
in
Bi-containing
Bi3+ is always situated at the perovskite A-site, thus allowing the location of a
magnetic transition metal cation at the B-site, i.e. with a partially occupied outer
electron d shell. The electronic configuration of the B-cations, in particular the
occupancy of their d-orbitals, is highly related to the magnetic properties, as will be
described later on. Note that as d-states correspond to the orbital angular quantum
number l = 2, they consist of 5 orbitals, 2l + 1. In absence of interactions all d-states are
energetically degenerated. However, in perovskite oxides the surrounding oxygen
14
Chapter 1. Introduction
octahedron of the B-site splits them into two energy states: high-energetic two eg
orbitals (z2 and x2-y2) and the low-energy three t2g orbitals (xy, xz and yz) [30]. This
splitting comes as a consequence of the electrostatic repulsion (note that eg orbitals
point directly toward the oxygen anions, whereas t2g do not), as shown in Fig. 1.6. This
effect is known as crystal field.
Fig. 1.6 – Energy splitting of the d-orbitals of a transition metal cation, B, in BO6
octahedron of ABO3 perovskite oxide. The d orbital images are reproduced from Ref.
[30].
15
Chapter 1. Introduction
Unless the crystal field is too strong, electrons in d-orbitals are placed as further
apart as possible, i.e. occupying different d-orbitals, so as to minimise their electrostatic
repulsion. Moreover, the first Hund’s rule states that electrons in d orbitals minimize
their energy in a parallel spin alignment, i.e. the ground state of the magnetic ion has the
maximum possible spin S.
The magnetic moment of an ion is given by m ∼ g J μ B J , where μB is the Bohr
magneton, gJ is the Landé g-factor and J is the total angular momentum J = L + S ( L
and S are the orbital angular and spin angular momentum, respectively). Yet in
transition metal ions, due to the non-degeneration of the d states, the orbital angular
momentum barely contribute to the magnetic moment of the ion, L is said to be
‘quenched’. Consequently, the magnetic moment comes almost entirely from the spin
angular momentum of the ion, i.e. m ∼ g e μ B S , where ge is the dimensionless electron
spin g-factor, which is close to 2.
The magnetic interaction between localised spins, Si (the bold notation denotes
vector character), is given by the exchange interaction of Heisenberg model, the
Hamiltonian of which is given by H = −
1
∑ J ij Si ⋅ S j . Since B-site cation chains in
2 ij ,i ≠ j
perovskites are interrupted by oxygen anions, direct magnetic exchange is weakened.
Magnetic interactions are mediated by the adjacent oxygen ions by the so-called
superexchange interaction, involving B – O – B bonds. Whether superexchange
interaction is ferromagnetic or antiferromagnetic depends, to a large extent, on the
filling of the eg orbitals according to the Goodenough-Kanamori’s (GK) rules [22].
Bearing in mind (i) the Pauli’s exclusion principle stating that two electrons in the same
orbital must possess antiparallel spins, and (ii) the Hund’s rule stating that electrons in d
orbitals minimize their energy in a parallel spin alignment, Goodenough-Kanamori’s
rules can be deduced as following:
a)
Either B (empty eg orbitals) – O – B (empty eg orbitals) or B (half-filled
eg orbitals) – O – B (half-filled eg orbitals) give rise to weak and strong
antiferromagnetic interactions, respectively [Fig. 1.7(a,b)].
16
Chapter 1. Introduction
b)
B (empty eg orbitals) – O – B (half-filled eg orbitals) give rise to
ferromagnetic interaction [Fig. 1.7(c)]
Note that these GK rules are deduced in the simplest scenario, i.e. in an ideal
perovskite where B – O – B bond angle is 180º. Distorted perovskites, rotation of the
oxygen octahedral, different B – O – B bond angles, etc, may give rise to different
magnetic interactions [22].
Fig. 1.7 – Schematic representation of 180º-bond-angle B – O – B superxchange
interaction in ABO3 perovskite. Depending on the occupation of the eg orbitals, the sign
of the magnetic interaction can be antiferromagnetic (a, b) or ferromagnetic (c).
As the B-site is occupied by only one kind of ion in perovskite oxides and, in
general, with the same oxidation state, i.e. having the same eg orbital filling,
antiferromagnetic interactions are much more common than the ferromagnetic ones. For
17
Chapter 1. Introduction
this reason, most multiferroic BiBO3 are antiferromagnetic. Instead, by combining two
different transition metal cations at the B-site, i.e. the so-called double perovskites
oxides Bi2 BB’O6, ferromagnetic paths can be engineered by choosing appropriately the
B, B’ magnetic ions, i.e. accomplishing B (empty eg orbitals) – O – B’ (half-filled eg
orbitals). But even if it is the antiferromagnetic interactions that dominate in a specific
double-perovskite, ferrimagnetism is likely to occur due to the fact that each transition
metal ion possesses different magnetic moment (different spin S), thus producing net
magnetisation because of the non compensation of the magnetic moments. For this
reason, Bi-based double perovskite oxides tend to be either ferromagnetic or
ferrimagnetic, displaying net magnetization.
1.2.4
The BiMnO3 system
BiMnO3 is a metastable compound, which requires high pressures (ranging from ~3
GPa to ~6 GPa) and relatively high temperatures (~600ºC to 700ºC) to be synthesize as
bulk polycrystalline samples [16, 31 – 34]. BiMnO3 was also synthesised in thin film
[35 – 39], where the high-pressure requirement for the metastable phase stabilization is
replaced by the epitaxial stress imposed by the substrate (see Sect. 1.3).
Temperature
Phase information
> ~770 K
Pbnm orthorhombic structure (centrosymmetric)
Non-centrosymmetric structure, monoclinic C2
[am ~ 9.58 Å, bm ~ 5.58 Å, cm ~ 9.75 Å and β ~ 108]
Non-centrosymmetric structure, monoclinic C2
[am = 9.532 Å, bm = 5.605 Å, cm = 9.854 Å and β = 110.7º]
Spins of Mn3+ ions order ferromagnetically
< ~770 K
< ~450 K
< ~105 K
Table 1.3 – BiMnO3 phases and phase transition temperatures from Ref. [16]
BiMnO3 would be expected to crystallize in an orthorhombic structure, similar to
LaMnO3, as La3+ and Bi3+ have very similar ionic radii [40]. In contrast, at low
temperatures, it crystallizes in a highly distorted non-centrosymmetric monoclinic C2
structure [31] due to the stereochemical activity of Bi cations [29], with cell parameters:
am = 9.532 Å, bm = 5.605 Å, cm = 9.854 Å and β = 110.7º [31]. 8 formula units,
BiMnO3, are contained in the monoclinic unit cell. BiMnO3 can equivalently be
described as a triclinic lattice (at ≈ ct ≈ 3.935 Å, bt ≈ 3.989 Å, α ≈ γ ≈ 91.46º, β ≈ 90.96º)
18
Chapter 1. Introduction
[34], containing one formula unit. This pseudocubic representation (note that the angles
are close to 90º) is usually used regarding BiMnO3 thin films, as will be discussed in
chapter 4.
At high temperatures, BiMnO3 undergoes two phase transitions at ~450 K and ~770
K, respectively [16], as listed in table 1.3. The first structural change (~450 K)
undergoes from a low temperature non-centrosymmetric monoclinic C2 structure to a
high temperature non-centrosymmetric monoclinic C2 structure, i.e. still allowing
ferroelectric order. Instead, the phase transition occurring at ~770 K leads to a
centrosymmetric structure (at higher temperatures), corresponding to a Pbnm
orthorhombic structure, which no longer allows spontaneous polarization.
Fig. 1.8 – Calculated electron localization of the
theoretical C2/c structure, where the yellow lobes
indicate the lone pair electrons on the Bi cations
(indicated as solid black round symbols),
reproduced from Ref. [41]. Note that the lone
pair dipoles cancel each other.
Thus, ferroelectricity in BiMnO3 might exist well above room temperature, up to
~770 K, which is usually considered the ferroelectric Curie temperature. Polarization
hysteresis loop as a function of the applied electric field were reported for
polycrystalline sample, though producing very small remanent polarisation values (of
the order of nC/cm2) [32]. However, some revised analysis of the crystal structure [42,
43] and first principles calculations [41] have questioned the non-centrosymmetric
structure of BiMnO3, indicating that the crystal structure is centrosymmetric monoclinic
C2/c and pointing to an antiparallel arrangement of the electric dipoles of the lone-pair
19
Chapter 1. Introduction
electrons of Bi3+ (Fig. 1.8) [41]. On the other hand, the four-resistive states reported for
La-doped BiMnO3 multiferroic tunnel junctions [4] can only be understood in the frame
of a ferromagnetic and ferroelectric material, strongly indicating a ferroelectric
behaviour of BiMnO3, at least in thin film form. Note that the epitaxial stress (see Sect.
1.3) may modify the structural characteristics and consequently the functional
properties. Additionally, nonlinear optical measurements on BiMnO3 thin films have
revealed changes in the polar symmetry of second harmonic generation signal by
applying electric fields, consistent with changes in the ferroelectric domain structure
[44].
Fig. 1.9 – Splitting in energy of the d-orbitals of Mn3+ due to the MnO6 octahedron and
the further Jahn-Teller distortion.
The magnetic behaviour of BiMnO3 arises from the magnetic superexchange
interaction Mn3+ – O – Mn3+. Note that Mn3+ is a d4 transition metal ion. Following the
Hund’s rule, the four electrons occupy the d-orbitals maximising the total spin, as
shown in Fig. 1.9, i.e. Mn3+ d-orbital configuration is (t2g3, eg1). The system reduces its
energy by slightly elongating the BO6 octahedron, the so-called Jahn-Teller distortion,
as it reduces the Coulomb electrostatic repulsion of the surrounding oxygen anions over
the occupied eg orbital (Fig. 1.9). This distortion is usually found for d4 and d9 transition
20
Chapter 1. Introduction
metal ions in octahedral coordination, which results in the energy splitting of the eg
orbitals: z2 and x2-y2 (it also splits t2g states, which are no longer degenerated).
Fig. 1.10 – Ferromagnetic coupling in BiMnO3
According to the GK rules (see Fig. 1.7), for an ideal perovskite, Mn3+ – O – Mn3+
superexchange interaction can be either ferromagnetic or antiferromagnetic, the latter
having much higher probability. Indeed, similar compound LaMnO3, being Mn ion also
trivalent, is antiferromagnetic. Despite this fact, in BiMnO3 is found that two out of
three Mn – O – Mn orbital configuration favour the ferromagnetic interactions (Fig.
1.10), which results in an overall long-range ferromagnetism, overcoming the
antiferromagnetic interactions [31]. This orbital ordering has been proposed to be due to
the highly distorted monoclinic structure because of the stereochemical active Bi3+. In
fact, Mn – O – Mn bond angles are significantly smaller than ideal 180º (between 140º
and 160º) [31]. Ferromagnetism in BiMnO3, which orders below 105 K [32], is quite
exceptional among insulator single perovskite oxides.
The theoretic magnetic moment of Mn3+ (spin S = 2) is 4 μB, thus BiMnO3 is
expected to show a saturated magnetisation of 4 μB/f.u., where f.u. denotes formula unit.
Yet the recorded for BiMnO3 bulk samples were slightly smaller, ~3.6 μB/f.u. [16], but
even lower for thin films [36].
The p orbitals of oxygen couple with d orbitals of magnetic ions, at the same time
form a covalent bond with p orbitals of Bi3+. On the other hand, oxygen anions are
responsible for the lobe-like distribution of the lone pair electrons of Bi3+. Hence, the
magnetoelectric coupling between the two ferroic properties in BiMnO3, if it is
21
Chapter 1. Introduction
produced, is to be produced indirectly. The magnetoelectric properties will be discussed
in chapter 4.
1.2.5
The Bi2NiMnO6 system
Bi2NiMnO6 is double-perovskite oxide, i.e. it combines two cations at the B-site in
a 3D rock-salt ordered pattern (as described later on). It is a metastable compound, like
BiMnO3, and high pressures (6 GPa) as well as relatively high temperatures (~800ºC)
were required to synthesize bulk polycrystalline samples [44]. Bi2NiMnO6 was also
synthesised in thin film [46, 47], where the high-pressure requirement for the metastable
phase stabilization is replaced by the epitaxial stress imposed by the substrate (see Sect.
1.3).
Temperature
> ~485 K
< ~485 K
< ~140 K
Phase information
Centrosymmetric structure, monoclinic P21/c
[am = 5.4041 Å, bm = 5.5669 Å, cm = 7.7338 Å and β = 90.184]
Non-centrosymmetric structure, monoclinic C2
[am = 9.4646 Å, bm = 5.4230 Å, cm = 9.5431 Å and β = 107.8º]
Spins of Ni2+ and Mn4+ ions order ferromagnetically
Table 1.4 – Bi2NiMnO6 phases and phase transition temperatures deduced from Ref.
[45]
Similar to BiMnO3, Bi2NiMnO6 crystallizes in monoclinic C2 structure (the lattice
parameters are listed in table 1.4), which is non-centrosymmetric and hence allowing
spontaneous polarisation. In fact, lattice parameters of Bi2NiMnO6 are found to be close
to those of BiMnO3. Bi2NiMnO6 undergoes a phase transition at ~485 K, above which
the structure is indexed as centrosymmetric monoclinic P21/c [45]. The occurrence of
this phase transition with a dielectric anomaly suggested the ferroelectric transition
temperature be placed at that temperature [45] [Fig. 1.11(a)]. It was predicted that a
remanent polarisation between ~20 and ~30 μC/cm2 is to be attained in this compound
[45, 48, 49]. However, neither conclusive ferroelectric hysteresis loops nor ferroelectric
domain switching current measurements have been reported, probably due to high
leakage (more details are found in chapter 5).
22
Chapter 1. Introduction
Fig. 1.11 – Temperature dependence of the dielectric permittivity (a) and magnetization
(b) of bulk Bi2NiMnO6. Reproduced from Ref. [45]
According to GK rules (Fig. 1.7), for an ideal ferromagnetic coupling, the electronic
configuration of Ni and Mn cations should be divalent and tetravalent, respectively, i.e.
Ni2+ (t2g6, eg2) having half-filled eg orbitals whereas Mn4+ (t2g3, eg0) empty eg orbitals
(Fig. 1.12). However, this is a required condition, but not sufficient, for a long-range
ferromagnetism in the compound. It is additionally necessary that the first B-cation
neighbours of Mn4+ should be Ni2+ and conversely, i.e. it is necessary the alternation of
Ni2+ and Mn4+ cations along the pseudocubic directions of the fundamental perovskite
structure, [100], [010] and [001] forming B – O – B’ – O – B – O – B’ – .... chains of
ferromagnetic superexchange interactions (Fig. 1.13). Note that either Ni2+ – O – Ni2+ or
Mn4+ – O – Mn4+ result in antiferromagnetic superexchange interactions (Fig. 1.7). This
specific long-range B-site order is usually called rock-salt configuration of the Bcations, evoking the configuration of Na1+ and Cl-1 in the rock-salt mineral. For the sake
of simplicity, on the following, the term B-site order will refer, exclusively, to this type
of ordering.
23
Chapter 1. Introduction
Fig. 1.12 – Splitting in energy of the d-orbitals of Mn4+ and Ni2+ in BO6 octahedron of
perovskite oxides.
Fig. 1.13 – Scheme of the double-perovskite structure with long range B-site order in a
rock-salt configuration.
24
Chapter 1. Introduction
The stability of the B-site order is given, mainly, by two factors:
i)
The oxidation state of the B, B’ cations. The different oxidation state favours
long-range B-site ordering in order to avoid instable regions in the compound
of electric disequilibrium. The larger the valence difference, the more stable
the B-site order.
ii) The size of the B, B’ cations. The larger the difference in the ionic radii of the
B cations, the more stable is the B-site order in order to achieve a stable
crystal structure.
In Bi2NiMnO6, two configurations of the B/B’ cations are possible: Ni2+/Mn4+ and
Ni3+/Mn3+. The former promotes the B-site order, due to both the difference in oxidation
state and the difference in ionic radii (0.690 Å and 0.530 Å, respectively, in octahedral
coordination [40]). Instead, the latter is hardly expected to be ordered at the B-site on
having the same valence and more similar ionic radii: 0.56 Å (or 0.60 Å in the high-spin
configuration of Ni3+) and 0.645 Å, respectively, in octahedral coordination [40]).
On the other hand, it is worth noting that even if Ni3+/Mn3+ ordering was to occur
B-site order, the fact that at least one of the eg orbitals in both cations is half-filled (in
the high-spin configuration of Ni3+ two eg orbitals are half-filled), antiferromagnetic
interactions would be much more likely. Additionally, the d4 electron character of
Mn3+ should promote a Jahn-Teller distortion, as described for BiMnO3 (Sect. 1.2.4).
The theoretic magnetic moments of Ni2+ (spin S = 1) and Mn4+ (spin S = 3/2) are 2
μB and 3 μB, respectively. Thus, for a configuration Ni2+/Mn4+ and long-range B-site
order, Bi2NiMnO6 is expected to show a saturated magnetisation of 5 μB/f.u. According
to the reported data [45], Bi2NiMnO6 shows a very large saturated magnetization (~4
μB/f.u), close to the theoretical value, indicating that it is the Ni2+/Mn4+ configuration
that prevails and that B-site order is achieved. The Curie temperature was found to be
around 140 K (Fig. 1.11 (b)] [45].
The magnetoelectric coupling, if produced, in Bi2 NiMnO6 should be originated in a
similar way to BiMnO3. The magnetoelectric properties will be discussed in chapter 5.
25
Chapter 1. Introduction
1.2.6
La-doping in Bi2NiMnO6 system
In terms of experimental procedures, one of the main drawbacks one find when it
comes to synthesising Bi-based multiferroic oxides is the high volatility of Bi element,
which entails the use of relatively low temperatures in the synthesis process. Yet the
general metastable character of these compounds demands the use of high temperatures
to the synthesis process. These two antagonistic requirements greatly hamper the
synthesis of Bi-based multiferroic materials [50, 51].
One strategy to diminish the effect of the Bi volatility consists of partial
replacement of Bi3+ cations by La3+ cations at the A-site [51]. La3+ and Bi3+ cations
have very similar ionic radii (0.130 nm and 0.131 nm, respectively [40]), but the former
is slightly smaller. Thus, small La-doping gives rise to a slightly reduced unit cell
volume, exerting the so-called chemical pressure (equivalently to a negative hydrostatic
pressure) which contributes to prevent Bi3+ cations from desorption during the growth
process in thin films (see Sect. 1.3). Indeed, partial substitution of Bi3+ cations by La3+
cations has been proved to facilitate single-phase stabilisation in BiMnO3 thin films
[51].
Fig. 1.14 – Temperature (left) and magnetic field (right) dependence of bulk
(La1-xBix)Ni0.5Mn0.5O3 samples reproduced from Ref. [52]).
On the other hand, the solid solution (Bi1-xLax)2NiMnO6 is interesting in itself. Both
Bi2NiMnO6 and La2NiMnO6 compounds display B-site order, giving rise to long range
ferromagnetism [45, 53]. Yet the latter show more robust ferromagnetic properties as
26
Chapter 1. Introduction
the spins order at ~300 K. By increasing La content in (Bi1-xLax)2NiMnO6 it is proved to
significantly increase the ferromagnetic Curie temperature [52] (Fig. 1.14). Thus, one
way to improve the ferromagnetic properties of Bi2NiMnO6 might consist of doping it
by La.
Fig. 1.15 – Possible phase diagram of solid solution (Bi1-xLax)2NiMnO6 deduced from
reported data of La2NiMnO6, Bi2NiMnO6 and (Bi1-xLax)2NiMnO6 [45, 52, 53]. Square
blue symbols indicate the magnetic Curie temperature as a function of La-content. The
dashed region indicates the possible morphotropic phase boundary. The dashed line
indicates the possible phase transition temperature.
The crystal structure of the solid solution (Bi1-xLax)2NiMnO6 remains noncentrosymmetric (monoclinic C2) for x ≤ 0.2 [52]. For x ≥ 0.3 (Bi1-xLax)2NiMnO6 can
be indexed as centrosymmetric monoclinic P21/c [52], which coincides with the crystal
structure of the high-temperature paraelectric phase of Bi2NiMnO6 (see Sect. 1.2.5).
Thus, ferroelectric order can only be enabled for 20% of La substitution, limiting the
possibilities of obtaining multiferroicity. In Fig. 1.15 a possible phase diagram of (Bi1xLax)2NiMnO6
is shown. It is to be noted, though, that the ferroelectric character of
monoclinic C2 phase of Bi2NiMnO6 is to be conclusively proved.
27
Chapter 1. Introduction
Interesting enough, La3+ is not a stereochemical active ion, thus not involved in the
ferroelectric distortion. Hence, increasingly La-content (up to x ~ 0.2) may
monotonously diminish the ferroelectric response of (Bi1-xLax)2NiMnO6 and might
eventually reduce the ferroelectric Curie temperature. Conversely, La-doping increases
the magnetic transition temperature, as seen in Fig. 1.14. Therefore, La-content may
also be used to approach both transition temperatures, which, according to expression
1.3, may enable larger magnetoelectric coupling.
1.2.7 State-of-the-art of multiferroic Bibased perovskite oxides
1.2.7.1
Bi-based perovskite, BiBO3
Almost all BiBO3 perovskite multiferroics are antiferromagnetic, with the unique
exception of BiMnO3. Therefore, BiMnO3 may be one of the most prominent
multiferroics, together with BiFeO3, which is the only known single phase compound
which display multiferroicity at room temperature.
No other multiferroic material has been as more extensively studied than BiFeO3,
because its multiferroic properties are robustly maintained well above room
temperature. The crystal structure of BiFeO3 is rhombohedral R3c [54], which is a polar
group and thus permitting the establishment of ferroelectric order. Indeed, the
ferroelectric transition temperature was proved to be very high, TFE = 1103 K, above
which a centrosymmetric paraelectric phase with space group R 3c can be indexed [55].
The polar axis is found along the [111] direction and a large saturated polarization, ~80
– 100 μC/cm2, is reported as expected for a high-Curie temperature ferroelectric [56].
On the other hand, BiFeO3 has a complicated magnetic behaviour, which is still on
debate. It is antiferromagnetic with G-type antiferromagnetic arrangement and a Néel
temperature of ≈ 620 K [57]. Additionally, superimposed on the antiferromagnetic
order, an incommensurate cycloidal spiral arrangement of the spins with a long period
of 620 Å was reported [58]. Moreover, the symmetry of the BiFeO3 structure allows
small canting of the spins, which gives rise to a net magnetization in terms of weak
28
Chapter 1. Introduction
ferromagnetism of the Dzyaloshinski-Moriya type [59]. This weak ferromagnetism was
confirmed experimentally, recorded a magnetisation value of around ~0.1 μB/f.u [60].
Other Bi-based perovskites have been proposed and proved to be multiferroic, but
all of them are antiferromagnetic with only weak ferromagnetism at most. First
principles calculations predicted BiCrO3 to be antiferroelectric and antiferromagnetic
[61]. Experimental results show weak ferromagnetism (~0.05 μB/f.u. saturated
magnetization) ordered below ~120 K in bulk [62] and thin film samples [63], but
contradictory conclusions were made about whether BiCrO3 is antiferroelectric [64] or
ferroelectric [63]. Another potential multiferroic is BiCoO3, which was predicted to
crystallize in tetragonal structure with large tetragonality c/a giving rise to huge
polarization (~180 μC/cm2) [65]. The structure was confirmed by neutron diffraction
[66], though the ferroelectric character has not been experimentally confirmed yet.
Furthermore, BiNiO3 has been considered, in which, despite being antiferromagnetic, a
weak ferromagnetism ordered below 300 K due to the spin canting, which is a
consequence of the small Ni – O – Ni bond angles [67]. Due to the preferred Ni2+
valence state, BiNiO3 displays an unusual charge disproportionation at the A-site of Bi3+
– Bi5+. This is quite rare for Bi cations and, in BiNiO3, affects the magnetic symmetry
of the compound [67]. Still, there is no experimental evidence of its ferroelectric
character and indeed structural analysis reveals BiNiO3 to be centrosymmetric [68].
1.2.7.2
Bi-based double-perovskite, Bi2BB’O6
Bi-based double-perovskites have been much less studied than their counterpart
perovskites. As aforementioned, according to the Goodenough-Kanamori’s rules, these
oxides have the advantage to allow engineering ferromagnetic paths nearly à la carte,
mainly corresponding to B – B’ cations being either d3 – d5 or d3 – d8, respectively, as
long as B – O – B’ bond angle is close to 180º [22]. Still, due to the different oxidation
states transition metal ions may take, obtaining the desired electronic configuration of B
and B’ cations has been in general difficult. Moreover, as stated in Sect. 1.2.5, longrange ferromagnetism requires B, B’ cations to be ordered alternatively along the
fundamental perovskite directions (Fig. 1.13). This has also been proved to be an
important challenge. Indeed, among all Bi-based double-perovskites, Bi2NiMnO6 is the
one confirmed to display rock-salt B-site order.
29
Chapter 1. Introduction
Bi2 FeMnO6 is predicted to crystallize in monoclinic C2 structure [69], but bulk
samples are usually indexed as orthorhombic [70]. Both Fe and Mn are found to be
mainly in a 3+ valence state, which hinders long-range B-site order [69 – 71]. A
hypothetical rock salt configuration would entail either ferromagnetic or more likely
antiferromagnetic exchange with a net magnetization of 1 μB/f.u. in a ferrimagnetic
compound (the magnetic moments of Fe3+ and Mn3+ are 5 μB and 4μB, respectively). Yet
the recorded magnetization values are much lower, thus confirming the lack of B-site
order in this compound [69 – 71]. On the other hand, Bi2FeMnO6 was proved to be
ferroelectric, displaying a quite large saturated polarization (~30 μC/cm2 at 150 K) [72].
Ab initio calculation predicted Bi2 FeCrO6 to show a large saturated polarization (≈
80 μC/cm2) and a saturated magnetization of 2 μB/f.u. for a rock salt configuration of
Cr3+ and Fe3+ [73]. Note that although ferromagnetic superexchange interaction is
expected for transition metals in d3 and d5 orbital configuration, Fe3+ – O – Cr3+ was
predicted to couple antiferromagnetically [73]. With no compensated magnetic
moments (5 μB and 3 μB for Fe3+ and Cr3+, respectively) a net magnetization would be
recorded (2 μB/f.u.). However, long-range B-site order in Bi2FeCrO6 is not likely to
occur due to the same charge of Fe3+ and Cr3+ and the similar ionic radii (0.645 Å and
0.615 Å, respectively [40]). Indeed Bi2 FeCrO6 is found to exhibit low magnetization (<
0.2 μB/f.u.) in both bulk samples [74] and thin films [75]. Nonetheless, some recent
experimental results show a certain thickness dependence of the B-site order, pointing
out that partially ordering of Fe3+ and Cr3+ can be improved by decreasing the thickness
of Bi2 FeCrO6 films [76]. The ferroelectric properties were confirmed experimentally,
showing the predicted large polarization of ≈60 μC/cm2 along [001] direction at ≈ 77
K), which would result in ~100 μC/cm2 along the polar axis [111] [75].
To date all Bi containing multiferroic double perovskite oxides consist of 3d
transition metals occupying the B-site, like Ni, Mn, Fe, ... Recently it was predicted,
though, that combining 3d and 5d transition metals at the B-site in Bi-based double
perovskites could allow robust room temperature ferrimagnetism to be attained [77]
(which is still a big challenge in multiferroics). In particular, Bi2NiReO6 and
Bi2MnReO6 are expected to order ferrimagnetically below 360 K and 330 K,
respectively. Although they would not be ferroelectric in the ground state, the
ferroelectric phase is likely to be stabilized in thin films by small percentages of strain
30
Chapter 1. Introduction
[77]. Still, these materials have not been synthesized so far, hence their predicted
multiferroic properties remain to be confirmed experimentally.
A summary of the ferroic properties of reported Bi-based multiferroic perovskite
oxides is given in table 1.4
31
Chapter 1. Introduction
Bi-based
Magnetic Ferroelectric
magnetic
order
order
perovskite oxide
BiMnO3
FM
FE
BiFeO3
AFM
FE
BiCrO3
AFM
?
BiCoO3
AFM
BiNiO3
AFM
×
Bi2NiMnO6
FM
FE
Bi2 FeMnO6
AFMb
FE
Bi2 FeCrO6
AFMb
FE
Bi2NiReO6
FiM
×
Bi2MnReO6
FiM
×
a
a
c
M
(TFM)
M*
(TNéel)
3.6 μB/f.u.
(105 K)
0.1 μB/f.u
(620 K)
0.05 μB/f.u
(120 K)
? μB/f.u
(470 K)
? μB/f.u
(300 K)
FE
P
(TFE)
0.13 μC/cm2
(770 K ?)
100 μC/cm2
(1103 K)
?
c
180 μC/cm2
(? K)
×
c
4.5 μB/f.u.
(140 K)
0.7 μB/f.u
(600 K)
0.2 μB/f.u
(130 K)
1 μB/f.u
(360 K)
2 μB/f.u
(330 K)
20 μC/cm2
(485 K)
30 μC/cm2
(250 K ?)
60 μC/cm2
(250 K ?)
×
×
Table 1.5 – Summary of the ferroic properties of Bi-based multiferroic perovskite
oxides. FM, AFM, FiM, FE stand for ferromagnetic, antiferromagnetic, ferrimagnetic
and ferroelectric order. M, M* and P denote the highest recorded value (either in thin
film or in bulk) for the magnetisation; magnetisation in AFM compound due to
ferrimagnetism, spin canting or other unconventional mechanisms; and polarisation,
respectively. TFM, TNéel, TFE are the ferromagnetic Curie temperature, the Néel
temperature and the ferroelectric Curie temperature. aPredicted multiferroic material
(not synthesised yet). bNo B-site order is found. cPredicted remanent polarisation or
predicted ferroelectric order.
32
Chapter 1. Introduction
1.3
Epitaxial engineering
In terms of device fabrication and applications, it is obvious that synthesising
nanometric-thick films of functional materials (such as multiferroics) shows greater
advantages than macroscopic bulk specimens, as many devices, like tunnel junctions,
spin valves, thin film transistors, etc, are based on multilayer structures. Moreover, their
functional properties are generally enabled (or enhanced) when films behave like single
crystal. Hence, thin films are in general grown on a single crystal substrate with the aim
of forming the so-called epitaxial film (Fig. 1.16), i.e. they grow crystalline with a
preferred out-of-plane (perpendicular to the interface substrate-film) crystal orientation
of the film unit cells (out-of-plane textured) and by maintaining the same relationship of
the in-plain (contained at the interface) crystal orientations of the film unit cells with
regard to the crystal orientations of the underlying substrate (in-plane textured). Note
that Fig. 1.16 depicts one specific case of epitaxy as, in the aforementioned definition,
the in-plane lattice parameter of the film and that of the substrate do not have to be
identical, nor do the crystal directions of the film unit cells be following those of the
substrate, but they should keep the same relationship with regard to those of the
substrate.
Fig. 1.16 – Cross section (left) and top view (right) of an epitaxial thin film.
33
Chapter 1. Introduction
This section aims to describe the possibilities that growing thin films offer
regarding the bulk specimens in terms of physical properties and crystal structure
stabilisation.
1.3.1 Stabilisation of metastable
compounds
The work shown in this thesis is focused on BiMnO3 and (Bi0.9La0.1)2NiMnO6 thin
films, as will be commented in Sect. 1.4. In ternary Bi – Mn – O or the quaternary Bi –
Mn – Ni – O system, the different Bi, Mn and Ni oxides (such as Bi2O3, Mn2O3 or
NiO), individually, are much more stable than the complex compound either BiMnO3 or
Bi2NiMnO6, thus requiring high pressures (~3 GPa – ~6 Gpa) to be synthesised.
However, preparing these compounds in thin film on a single crystal used as a
substrate can ease this process, circumventing the high-pressure requirement, what is
called epitaxial stabilisation or stabilisation by epitaxial stress. Two main factors favour
the stabilisation of metastable compounds in thin films: (i) the use of lattice-matched
substrates, i.e. with similar lattice parameters to those of the compound that is to be
formed; (ii) the use of substrates with similar structure, i.e. with similar arrangement of
the ions to that of the compound to be formed, e.g. perovskite structure. Accomplishing
both criterions epitaxial thin films tend to be formed (Fig. 1.16).
To date, bulk specimens of BiMnO3, (Bi0.9La0.1)2NiMnO6 and Bi2NiMnO6 were all
polycrystalline structures. Thus, similar to a single crystal behaviour might be obtained
just by growing epitaxial thin films.
1.3.2
Epitaxial tuning
Epitaxial thin films might be grown strained on the substrate, which means that the
in-plane lattice parameter of film adopts the lattice parameter of the substrate (Fig.
1.17), the so-called coherent growth. The strain of the film is usually defined as:
34
Chapter 1. Introduction
ε=
a film − abulk
abulk
(1.7)
where abulk is the free-standing lattice parameter of bulk material, whereas afilm is the inplane lattice parameter of the film. Unit cell volume tends to be maintained in
crystalline materials, which entails an enlargement or a contraction of the out-of-plane
lattice parameter when the in-plane lattice parameter is compressive or tensile strained,
respectively (Fig. 1.17).
Fig. 1.17 – Growth of strained thin films
Strain, though, leads to stress in the material, with an energy cost. This energy cost
increases on increasing thickness, up to the point where it becomes energetically more
favourable to release the strain (by means of the formation of dislocations [78],
crystallographic domains [79] or even changing sample stoichiometry [80 - 82]). This
results in a relaxation of the film, i.e. recovering the bulk lattice parameter. A film is
said to be fully relaxed when its structure is identical to that of the bulk.
35
Chapter 1. Introduction
The constraints imposed by the substrate forces in-plane lattice parameters to be
fixed, apart from modifying it. Note that a cubic crystal structure of the substrate may
induce a tetragonal-like structure of the film in materials that not necessarily are
tetragonal. As a result the crystal structure and the crystal symmetry of the film may
severely change with regard to bulk specimens, and consequently the physical
properties.
Interesting enough is the effect epitaxial stress may produce on magnetic and
ferroelectric properties of Bi-based multiferroic thin films. Indeed, the phase diagram of
ferroelectric epitaxial thin films is noticeable modified as a function of strain [83 – 87].
In particular, BaTiO3 thin films show a strongly strain-dependent Curie temperature
[85]. But magnetic properties have also been reported to be altered, such as the reduced
Curie temperature of strained Bi2NiMnO6 thin films grown on SrTiO3 (~100 K) [46].
1.4
Outline of the thesis
This thesis aims to characterise the structural and functional properties of the
ferromagnetic Bi-based multiferroics, which, up to now reported, consist of BiMnO3
and Bi2NiMnO6 (see table 1.5). Specifically, this work is focused on the growth and
characterisation of BiMnO3 and (Bi0.9La0.1)2NiMnO6 thin films. The use of La-doping is
motivated by the reasons exposed in Sect. 1.2.6.
The films were grown by pulsed laser deposition (Sect. 2.1) onto single-crystal
substrates SrTiO3, (001)-oriented (i.e. with the [001] crystallographic direction lying
along the out-of-plane direction).
Chapter 2 describes the physical mechanisms of both the thin film growth process
and the experimental techniques and tools used to characterise the films.
Chapter 3 is focused on the ferroelectric measurements, dielectric/resistive and
magnetoelectric measurements. For these electric measurements parallel-plate
capacitors are fabricated, using Nb doped SrTiO3 as a bottom electrode and Pt as a top
electrode. Special attention is given to the conventional artefacts these measurements
36
Chapter 1. Introduction
often produce when performed on thin films. In particular, different simulations are
carried out considering the different source of these artefacts.
In Chapter 4 results of BiMnO3 thin films are shown. In particular, it is determined
the deposition conditions which enable stabilising single-phase formation. This has
turned out an elusive task due to the multi-phase tendency of these compounds and the
high volatility of Bi. A compositional study is carried out which enable to relate the
multiphase tendency with the Bi-deficiency. Structural study proves single-phase
BiMnO3 thin films grow fully coherent on SrTiO3 substrates, adopting a tetragonal-like
structure. The growth mode, though, is found, at any event, three-dimensional (3D).
Finally the ferromagnetic character is borne out and the electric/magnetoelectric
properties extracted following the precautions stated in chapter 3, demonstrating a weak
magnetoelectric coupling of these materials.
In Chapter 5 results of (Bi0.9La0.1)2NiMnO6 thin films are shown. Similar to
BiMnO3, these double-perovskite films show a multiphase tendency, although in a
lesser extent probably due to the La-doping. Fully coherent growth on SrTiO3 substrates
is also found, adopting a tetragonal-like structure. Unlike BiMnO3, (Bi0.9La0.1)2NiMnO6
thin films grow in 2D mode, up to a critical thickness, which enable very flat surfaces.
Importantly enough for the magnetic properties, (Bi0.9La0.1)2NiMnO6 thin films are
found to display long-range B-site order and the Ni2+/Mn4+ electronic configuration,
which gives as a result long-range ferromagnetism, but with a reduced Curie
temperature compared to bulk data. The ferroelectric domains switching current is
measured, which allows conclusively stating that (Bi,La)2NiMnO6 compounds are
indeed ferroelectric up to at least 10% La content. Nonetheless, the coupling of the
ferromagnetic and ferroelectric order was also proved to be weak.
37
Chapter 1. Introduction
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42
Chapter 2. Experimental Techniques and Data Analysis
Chapter 2
Experimental Techniques
and Data Analysis
43
Chapter 2. Experimental Techniques and Data Analysis
44
Chapter 2. Experimental Techniques and Data Analysis
2.1 Growth Techniques
2.1.1 Pulsed Laser Deposition
BiMnO3 and (Bi,La)2NiMnO6 thin films were grown by Pulsed Laser Deposition
(PLD). The system equipment is placed in the Departament de Física Aplicada i Òptica
(Facultat de Física, University of Barcelona) in the research group of Grup
d’Estructures en Capa Fina per a l’Espintrònica (GECFE).
PLD, the process of which is schematically depicted in Fig. 2.1, belongs to the set
of Physical Vapour Deposition techniques [1 - 3]. An intense ultraviolet laser pulse is
focused by means of external lens onto a bulk piece –called the target–, placed inside a
high vacuum chamber, which contains the oxide mixture with the desired composition
of the compound to be studied (see target fabrication 2.1.3). The relatively high energy
of the laser pulse concentrated on a small area (typically 1 – 3 J/cm2) in a short period of
time (around a few tens of nanoseconds) leads the material of the target to be ejected,
forming a high-energetic plasma (called ‘plume’). In the near-vacuum the ablated
material expands to the substrate which is located in front of the target, at a few
centimetres away. The film is formed pulse after pulse as the ejected material is
condensed on the relatively cold substrate. The plume of the ejected material is very
directional, as cosnφ (8 < n < 12) [1 - 3], which prevents large areas from being
uniformly covered.
High energy photons are used, in the ultraviolet range, as the absorption coefficients
of most non-metallic materials tend to increase the shorter the wavelength of the photon
is. That makes the ablation process take place only in the very near surface of the target,
avoiding heating large volumes of the target by the laser pulses and promoting a high
energy transfer. There is a threshold in the so-called fluency, i.e. the energy per area of
the coming laser pulses onto the target, from which the absorbed energy is higher than
that needed for material emission. Thus, above the ablation threshold, the emission
process is not controlled by the vapour pressure of the target species and, consequently,
the ejected material preserves the stoichiometry of the target. For this reason PLD has
been widely used to grow complex multi-cation oxide compounds such as
45
Chapter 2. Experimental Techniques and Data Analysis
superconducting materials like YBa2Cu3O7 [4], ferroelectric materials like BaTiO3 [5]
and magnetic materials like (La,Sr)MnO3 [6]. Very often O2 is introduced for oxides
growth in order to compensate for oxygen desorption from the growing film during the
deposition process and hence achieve the right oxidation state of the cations.
Fig. 2.1 – Schematic representation of the PLD system.
2.1.2 Thin film growth process
Our pulsed laser deposition system, described in Fig. 2.2, consists of a KrF excimer
laser source (Lambda Physik LPX-210), emitting light pulses of 34 ns with a
wavelength of 248 nm. The laser beam is focused on the target with an incident angle of
45º. The deposition process takes place in a high vacuum chamber in which a pressure
lower than 10-5 mbar can be attained by using a mechanical and a turbomolecular
pumps. The gas management system enables O2 to be controllably introduced into the
chamber. The pressure is measured by means of two separate vacuum gauges depending
on the pressure range: one of thermal conductivity type (pirani) for high pressures (from
room pressure to 10-1 mbar) and the other one of cold cathode type (penning) for lower
pressures than 10-1 mbar. The target is mounted on a target-holder which can rotate
assisted by an electric motor. The substrate is heated by contact to an oxygen
46
Chapter 2. Experimental Techniques and Data Analysis
compatible holder –called the heater–, which is heated by Joule effect. Thermal
conducting silver paste is used to stick the substrate onto the heater in order to ensure
good thermal transfer. The temperature is measured by a thermocouple placed inside the
heater. Electronic PID (Proportional-Integral-Derivative controller) system is used to
monitor the supplied electric power to the heater, aimed at achieving a stable
temperature for the growth process.
Fig. 2.2 – PLD system and laboratory where samples have been grown
The growth process consists of several stages. First, high vacuum is reached in the
deposition chamber in order to ensure no impurity coming from the atmosphere. The
substrate is heated, afterwards, up to the deposition temperature, whereas the desired O2
pressure is reached by controlling the O2 flow. When substrate temperature is stabilised,
the rotating target is hit by around 150 pre-ablation laser pulses in order to eliminate
impurities that may be present on the surface. A shutter in front of the target inhibits the
material ablated in the ‘cleaning’ process from arriving to the substrate. After the preablation process, the shutter is removed and the deposition starts, keeping the target
rotating. The number of laser pulses is set before the deposition process takes place. The
rotation of the target is essential to achieve a homogeneous plume of the ablated
material and to ensure uniform erosion of the target. Otherwise, stoichiometry as well as
density of the target surface may be quicker altered when hitting the laser pulses on the
same spot [1 – 3]. When deposition finishes, the sample is immediately cooled down
(except when annealing is applied) under full O2 pressure (~1 bar). The purpose is, apart
from minimising bismuth desorption from the film during the cooling process,
oxygenating the sample in order to reach the appropriate oxidation state of the transition
metal cations. The PLD deposition parameters are summarised in table 2.1.
47
Chapter 2. Experimental Techniques and Data Analysis
Deposition Parameter
Setting
Laser fluence
1.5 J/cm2 – 2.5 J/cm2
Pulses frequency
1 Hz – 10 Hz
Substrate temperature
590ºC – 700ºC
O2 deposition pressure
0.05 mbar – 0.60 mbar
Target-to-substrate distance
5.0 cm
O2 cooling
1.0 bar
Annealing
0 hour – 2 hour @ 450ºC, 1 bar O2
Table 2.1 – Overview of the deposition parameters
After every deposition process the target should be polished in order to ensure that
the irregularities in the surface morphology caused by the hit of the laser pulses are
eliminated and the original stoichiometry and morphology recovered.
2.1.3 Target fabrication
The targets used for the growth of BiMnO3 and (Bi,La)2NiMnO6 were made in
Institut de Ciència de Materials de Barcelona (ICMAB, CSIC) and the Departament de
Ciència de Materials i Enginyeria Metal·lúrgica (Facultat de Química, University of
Barcelona).
The pellets were produced from mixing the primary oxide powders, i.e. Bi2O3
(99.99 % pure) and MnO2 (99.90 % pure) for BiMnO3; Bi2O3 (99.99 % pure), La2O3
(99.90 % pure), MnO2 (99.90 % pure) and NiO (99.0 % pure) for (Bi,La)2NiMnO6. The
oxide powders were obtained from the commercial company Alfa Aesar .The process
consists of several steps:
1) The powders are weighted according to the stoichiometry needed for BiMnO3
and (Bi,La)2NiMnO6, except for Bi2O3, in which an excess around 10 % is used
in order to compensate for the high Bi volatility. In the case of La2O3, which is
high hydrophilic, it is heated for 12 hours at 1000ºC before weighting in order to
48
Chapter 2. Experimental Techniques and Data Analysis
evaporate the water content and preventing stoichiometry deviations in
(Bi,La)2NiMnO6 targets.
2) The powders are mixed for one hour in an agatha mortar aimed to homogenise
the oxides and reduce the volume of the powder particles so as to maximise the
surface of them. This will increase the homogenisation of the different oxides in
the posterior thermal treatment.
3) The mixture is hydraulically pressed in a slow continuous process up to
attaining 10·103 kg/cm2.
4) The pressed pellet is temperature treated, i.e. it is heated inside an alumina
crucible up to 500ºC for 15 hours (with a 5ºC/min increasing and decreasing
ramps).
5) The pellet is again homogenised and step 2) and 3) are repeated. Then the
thermal treatment is applied as in step 4) but up to 600ºC for 15 hours.
6) Finally, the process 2), 3) and 4) is repeated for a third time, but with a thermal
annealing of 700ºC for 15 hours. The repetition of the process ensures to
achieve as homogeneous and dense target as possible.
The low temperature used in the thermal treatments, compared to the fabrication of
common oxide targets, aims to minimise Bi evaporation and hence preserving the
desired target stoichiometry. But, as a consequence, the target does not contain the
compound itself, i.e. BiMnO3 or (Bi,La)2NiMnO6, but the mixture of the primary
oxides. The compound is formed in the PLD process by the epitaxial pressure induced
by the substrate onto the coming ablated stoichiometric material (see section 1.3.1).
2.2 Structural characterisation
techniques
2.2.1 X-ray diffraction
X-ray diffraction (XRD) is a powerful and thorough technique to study the structure
of materials. Lattice parameters, crystal symmetry, compounds and phases
identification, texture of the film, epitaxial relation with the substrate, etc, are some of
49
Chapter 2. Experimental Techniques and Data Analysis
the structural aspects of the samples that can be assessed by XRD. This technique is
based on the interference pattern produced by a monochromatic incident beam light
when interacts with a periodic structure, i.e. the periodic arrangement of the ions in a
crystalline material forming atomic planes (Fig. 2.3).
Fig. 2.3 – Schematic representation of the Bragg’s law.
For a given family of planes (hkl), interplanar distance dhkl, constructive interference
occurs when incident angle, θ, is such that accomplishes that the path difference of two
waves equals a multiple of the wavelength of the incoming radiation (see Fig. 2.3), the
so-called diffraction condition of the Bragg’s law:
2d hkl sin θ = nλ
(2.1)
where n is the order of diffraction and λ is the wavelength of the incoming X-ray
radiation, in our case the Kα1 line of copper: λ = 1.5406 Å.
The XRD experiments were performed on a four-circle diffractometer MRD
PANalytical placed at the Centres Científics i Tecnològics de la Universitat de
Barcelona (CCiTUB). It is to be noted that the X-ray beam reaching the sample in this
diffractometer is not full monochromatic as it also contains Kα2 and, in much lesser
extent, Kβ (Kβ is almost completely filtered) lines of Cu.
50
Chapter 2. Experimental Techniques and Data Analysis
Fig. 2.4 – Schematic representation of a four-circle diffractometer. nsurface is the vector
normal to the surface of the sample and n planes is the vector normal to the diffracting
(hkl) planes.
The four-circle geometry, depicted in Fig. 2.4, is very appropriate in the structural
characterisation of thin films, as it will be discussed later on. The four angles are
defined as follows:
ω is the angle between the incident beam and the plane of the sample surface. It is
modified by rotating the sample-holder around the axis which is parallel to the
sample surface and perpendicular to the diffraction plane (the plane containing the
incident and diffracted beam).
2θ is the angle between the incident beam and the diffracted beam. It is modified by
changing the position of the detector.
φ is the angle related to the rotation of the sample-holder around the axis normal to
the sample.
ψ is the angle between the diffraction plane and the axis normal to the sample
surface.
51
Chapter 2. Experimental Techniques and Data Analysis
Diffraction reflections
configuration
in
symmetric
and
asymmetric
When the XRD experiment is carried out under the restriction of θ = ω ,ψ = 0 , the
configuration is said to be symmetric. In this configuration only the planes which are
parallel to the surface of the sample contribute to the diffraction scan, as it is depicted in
Fig. 2.5 (a). The so-called 2θ-ω scan (also known by θ/2θ scan) is the most typical
symmetric scan, in which the sample angle, ω, and the detector position, 2θ, are
simultaneously rotated such us ω = (2θ)/2, i.e. coupled in such a way that the restriction
θ = ω is fulfilled. This kind of scan allows verifying weather the film has grown with a
preferred orientation, i.e. all the crystallites of the film grow with the same (hkl) planes
parallel to the surface or is polycrystalline (random distribution of (hkl) planes).
Additionally, 2θ- ω scans allows determining the interplanar distance, dhkl, of the atomic
planes parallel to the surface by using Bragg law (2.1), i.e. the out-of-plane lattice
parameter of the film (see Appendix A). On the other hand, 2θ-ω scans are also used to
to detect any diffraction reflection of any phase formed in the film growth and therefore
to assess whether the film has grown single-phase or not. Phases were identified using
Ref. [7].
Fig. 2.5 – XRD scan in (a) symmetric configuration (2θ-ω scan) and (b) in asymmetric
configuration
52
Chapter 2. Experimental Techniques and Data Analysis
The asymmetric configurations, in which ω ≠ θ and/or ψ ≠ 0 , enables the planes
that are not parallel to the surface of the sample to diffract and to be analysed, as it is
depicted in Fig. 2.5 (b). These XRD scans are widely used to characterise the in-plane
crystal structure of the film, e.g. the in-plane lattice parameter.
Texture of the films characterisation
A) Out-of-plane texture of the film
Fig. 2.6 – Schematic representation of (a) fully textured film and (b) mosaic texture
film and the corresponding rocking curves: (c) and (d), respectively
Although the film may grow with an out-of-plane preferred orientation, a certain
dispersion of the crystallites of the film occurs. The less dispersion the more texture
quality of the film (Fig. 2.6). A way to quantify this crystalline quality is by means of
the so-called Rocking curves (also known by ω scan), Fig. 2.6 (c and d). In this scan the
2θ angle of a given reflection peak is maintained fixed while the ω angle is swept
around ω = θ within a short range. Thus, narrow Rocking curve peaks, characterised by
full width at half maximum (FWHM), become a figure of merit of the crystal quality of
the films.
53
Chapter 2. Experimental Techniques and Data Analysis
B) In-plane texture of the film and cube-on-cube growth
Fig. 2.7 – (a) and (b) top planar view for in-plane textured films (red dashed line) on
substrate lattice (blue solid line). In picture (b) a particular case of in-plane textured
film is depicted: cube-on-cube growth.
The in-plane texture of the film that is the relative orientation of the unit cell of the
film compared to that of the substrate can be assessed by asymmetric configuration
[Fig. 2.5 (b)] by the so-called φ scans and pole figures as described in the following.
φ scans consists of rotating 360º the φ angle (Fig. 2.4) for a an asymmetric
reflexion, in which 2θ and ω angles are fixed fulfilling the Bragg’s diffraction
condition for the given asymmetric reflexion. As ω = θ is accomplished, ψ is
tilted in order to enable the asymmetric planes to be in the diffraction plane.
When the film is in-plane textured, the φ scan will produce as many diffraction
peaks as the in-plane symmetry of the film, e.g. a cubic or tetragonal symmetry
with the a axis perpendicular to the axis normal to the sample must reproduce 4
diffraction peaks on φ being rotating 360º. Additionally, when the angular
position of the film diffraction peaks are coincident with the angular position of
the substrate diffraction peaks, the growth mode is said to be cube-on-cube (Fig.
2.7 (b)).
54
Chapter 2. Experimental Techniques and Data Analysis
Pole figures is an extension of the φ scans, in which for each ψ value a φ scan is
performed, giving rise to a 2D in-plane diffraction map.
The film is called to grow epitaxial when grows in-plane and out-of-plane textured.
Reciprocal space maps
Reciprocal space maps are used to determine the epitaxial relationship and the
lattice parameters of the film, as will be described in the following.
Fig. 2.8 – (a) Reciprocal space vector qhkl and the relationship with the angles (θ, ω);
(b) Schematic description of a q-plot scan.
Let’s define the vector qhkl as the reciprocal space vector of the family of planes
(hkl). A condition of reciprocal space vector is to be perpendicular to the planes (hkl), as
depicted in Fig. 2.8 (a). Moreover, next expression is also satisfied:
1
qhkl =
d hkl
where dhkl is the distance between the planes (hkl). Thus, | qhkl | units are [m-1].
55
(2.2)
Chapter 2. Experimental Techniques and Data Analysis
Being a, b, c the lattice parameters of a crystal structure, one can describe a vector
base of the real space a , b , c , from which the vector base of the reciprocal space, a * ,
b * , c * , can be defined as follows:
*
*
c×a
b ×c
a ×b
*
a = ; b = ; c = a ⋅ (b × c )
a ⋅ (b × c )
a ⋅ (b × c )
(2.3)
Once defined the reciprocal space base, the reciprocal space vector qhkl can be written
as qhkl = ha * + kb * + lc * . When a , b , c vectors are orthogonal, that is for cubic,
tetragonal and orthorhombic crystalline structure, then next expressions are fulfilled:
a * || a ;
b * || b ;
and it is satisfied: qhkl =
c * || c
1
a* = ;
a
1
b* = ;
b
1
c* =
c
(2.4)
h2 k 2 l 2
+
+
a 2 b2 c2
A general expression of qhkl for the different crystal structures is found in the
Appendix A.
In order to determine the in-plane parameter and the out-of-plane parameter is
useful to define qparallel and qperp as the parallel and perpendicular component of qhkl to
the surface of the sample, respectively. If we consider a and b the in-plane parameters
and c the out-of-plane parameter in an orthogonal base, then next expressions are
fulfilled:
h2 k 2
+
a 2 b2
q parallel =
q perp =
l
c
(2.5)
A reflexion of the type (h0l) tends to be used. Then, the expressions are simplified:
q parallel =
h
a
q perp =
56
l
c
(2.6)
Chapter 2. Experimental Techniques and Data Analysis
Fig. 2.9 – Reciprocal space map of film and substrate when (a) the film has grown
relaxed (bulk lattice parameters) and (b) the film has grown completely, adapting the
in-plane parameter to the substrate.
The determination of qhkl is carried out by the so-called q-plot scan (or reciprocal
space maps), which consists of doing a 2θ-ω scan for different values of ω of a given
asymmetric reflexion (otherwise only qperp could be determined), as depicted in Fig. 2.8
(b). It is necessary to relate the angles (θ, ω) to qparal and qperp. From the Bragg law, 2dhkl
sinθ = λ, and from Fig. 2.8 (a), next expressions can easily be deduced:
q parallel =
q perp =
2
sin θ sin(θ − ω )
λ
2
sin θ cos(θ − ω )
λ
(2.8)
The reciprocal space maps allow determination of qparallel and qperp of the Bragg
spots and thus to determine in-plane and out-of-plane cell parameters of the film and the
substrate. Consequently the epitaxial strain exerted by the substrate can be determined.
If the measured qparallel of the substrate and the film are coincident, as depicted in Fig.
2.9 (b), then the in-plane lattice parameter of film has adopted the substrate lattice
57
Chapter 2. Experimental Techniques and Data Analysis
parameter. In this case the film is said to grow coherently (fully strained) on the
substrate. On the other hand, when the measured qparallel of the film corresponds to the
bulk lattice parameter, then the film is said to grow fully relaxed, as depicted in Fig. 2.9
(a).
2.2.2 X-ray reflectivity
X-ray reflectivity (XRR) is a non-destructive and non-contact technique for
accurately determining the thickness of films in the range of 2 – 200 nm, with a
precision of about a few Å. In addition, this technique allows determining the roughness
and the density of the film or even multilayers. The XRR experiments were performed
on a Siemens D-500 diffractometer with grazing incident angle optics, placed at the
CCiTUB.
Fig. 2.10 – Sketch of the XRR experiment, where t is the thickness of the film, θ the
incident angle, and θD the diffracted angle.
XRR consists of irradiating the sample with an incident X-ray beam (λ of Kα1 of Cu
in our case) at grazing angles (small ω angle, Fig. 2.4) and collecting the reflected beam
in a detector (placed at 2θ angle, Fig. 2.4), very much alike to Fig. 2.4, accomplishing
the condition ω = θ and ψ = 0. As incident grazing angles are used much of the intensity
of the X-ray beam is reflected, being θc the critical incident angle, below which total
external reflexion occurs. θc depends on the electronic density of the material, with
58
Chapter 2. Experimental Techniques and Data Analysis
typical values below 0.5º. Above θc part of the incident radiation penetrates the film (see
Fig. 2.10), with a diffracted angle, θD, that is given by the Snell’s law, cosθ/cosθD = n =
cosθc, where n is the refraction index of the film. Due to the different electronic density
of film and substrate, reflection of the diffracted beam occurs at the interface. Thus, the
incident beam is reflected from both the top of the film (surface) and the bottom of the
film (interface), giving rise to constructive and destructive interference pattern
depending on the difference in the optical path (Fig. 2.10). Using trigonometry and the
Snell’s law, the interference condition, in which the optical path difference equals a
multiple of the wavelength, is given by [8]:
2 ⋅ t ⋅ sin 2 θ m − sin 2 θ c = m ⋅ λ
(2.9)
where t is the thickness of the film, θm is the incident angle at which constructive
(destructive) interference is produced and m is the order of the constructive (destructive)
interference.
In contrast to XRD, the refractive effects are significant at low incident angle
solely, becoming negligible for high θ. Thus, XRR experiments are normally performed
as a coupled θ/2θ scan up to 2θ < 6º, in which a pattern of interference fringes are
recorded above θc (Fig. 2.11). Eq. 2.9 can be rewritten as:
2
⎛ λ ⎞
2
sin 2 θ m = sin 2 θc + ⎜
⎟ ⋅m
⎝ 2⋅t ⎠
(2.10)
Extracting the position of the minima, θm, (or, equivalently, the maxima) of the
oscillations of interference (Fig. 2.11) and computing sin2θm, a linear dependence is
expected with the square of the order of the minima (or maxima), m2, Eq. 2.10. The
linear fit (Inset: Fig. 2.11) should give us both the thickness of the film (from the slope
of the fit) and the critical angle, θc.
59
Chapter 2. Experimental Techniques and Data Analysis
Fig. 2.11 – XRR spectrum of a 107 nm-thick (Bi0.9La0.1)2NiMnO6 film on SrTiO3
substrate. Inset: Fitting (solid line) of sin2θm vs m2 data (blue solid square symbols) and
sin2θm’ vs (m’)2 data (red open square symbols), where m and m’ are integer and
semiinteger numbers, respectively.
It is worth adding that if the refraction index of the substrate is larger than that of
the film, the X-ray beam reflected at the interface is inverted, i.e. is π-phase shifted. In
order to correct this shift, integer m in expression 2.10 is replaced by a semiinteger
number (m’ = m + 1/2), being Δm’ = Δm = 1 [8]. This small correction is shown in the
inset of Fig. 2.11 (open symbols) where sin2θm’ is plotted versus m’. As observed the
difference in thickness is small (around 1 nm over ∼100 nm of thickness), of the order
of 1.2 %.
2.2.3 Transmission electron microscopy
Transmission electron microscopy (TEM) uses the wave-like character of the
electron to obtain images of the explored materials, alike its optical counterparts but in a
nanometric scale due to the small electronic wavelength (~ 10-12 m) that follows the
energy range at which electrons are accelerated (typically 100 – 400 kV). Using
different operating modes TEM allows not only image formation (image mode) but also
registering diffraction patterns of selected areas of the sample (diffraction mode).
Additionally, TEMs are usually equipped by compositional analysis components (such
60
Chapter 2. Experimental Techniques and Data Analysis
as electron energy loss spectroscopy or energy dispersive spectroscopy), as it will be
discussed in section 2.4, which makes this technique very versatile.
However, samples need prior preparation for TEM analysis, i.e. they need to be
thinned down in order to enable electrons to pass through. The so-called TEM lamellas
of our samples were prepared by J. M. Rebled, Dr. S. Estradé and Dr. F. Peiró by
focused ion beam (FIB) in a FEI Strata dual beam system located at the CCiTUB.
Lamellas were prepared in cross section geometry, i.e. allowing characterising both
substrate and film.
The TEM process is schematically depicted in Fig. 2.12 (a). Electrons are produced
either thermoionically, by heating W or LaB6 cathode, or by field emission electron
gun, which generates electrons when exposed to an intense electric field. The latter has
the advantage of a more monochromatic electron source and a finer probe which gives
rise to a better resolution. The electron beam is accelerated and confined onto the
specimen by a condenser magnetic lens system. The transmitted electron-wave is
gathered by the objective lens, after which some intermediate lens allows choosing
between two basic operating modes:
Image mode. In this mode the transmitted electrons are gathered by the objective
lens and collected in the image plane [Fig. 2.12 (b)], where a preliminary image
is formed. The subsequent intermediate lens is focused on the image plane.
Finally the image is formed on the screen (or CCD camera) after further
magnification and the projector lens [Fig. 2.12 (a)].
Diffraction mode. In this mode, instead, the intermediate lens is focused on the
back focal plane of the objective lens [Fig. 2.12 (b)], where the diffraction
pattern of the sample is recorded. Thus, by changing the strength of the
intermediate lens, the operating mode can be switched from image mode to
diffraction mode and vice versa. The selected area diaphragm is usually used to
select specific regions of the TEM specimen, e.g. only a small region of the
substrate or substrate + film. This mode is called Selected Area Electron
Diffraction (SAED) and it is the one used in this work. Depending on the
crystallographic axis along which the cross section is prepared, different
61
Chapter 2. Experimental Techniques and Data Analysis
crystallographic planes are enabled to diffract. SAED patterns allow obtaining
information about the unit cell, the epitaxial relationship, etc.
Within image mode, obtaining higher contrast images is possible by introducing an
objective diaphragm in the back focal plane [Fig. 2.12 (a)], which permits selecting only
the transmitted beam [Fig. 2.12 (c)], so-called bright field images, or by tilting the beam
(or moving the aperture) only the diffracted beam [Fig. 2.12 (d)], so-called dark field
images. Usually dark field images have higher contrast, although the intensity is greatly
reduced.
Fig. 2.12 – (a) Scheme of TEM process. (b) Image plane vs back focal plane. Bright
field (c) and Dark field (d) mode for imaging.
Finally, special TEM techniques can also be performed as described in the
following. First, Scanning Transmission Electron Microscopy (STEM), which no longer
62
Chapter 2. Experimental Techniques and Data Analysis
consists of a static electron beam but, instead, the condenser lenses concentrate the
beam on a small spot size that can be scanned on the sample by means of scan coils.
STEM images have better contrast than conventional TEM images and they can also be
obtained either in dark field or in bright field mode. Second, High Resolution
Transmission Electron Microscopy (HRTEM), in which TEM images are formed by a
process called phase contrast. The contrast is formed by constructive and destructive
interference from the electron waves passing through a material showing a certain
periodicity (crystalline material). This phase-contrast technique allows obtaining much
information about the crystal structure of the material.
Both TEM and HRTEM images, as well as SAED patterns of film and substrate,
were obtained by J. M. Rebled, Dr. S. Estradé and Dr. F. Peiró in a Jeol 2010F field
emission gun TEM operating at 200 keVs located at the CCiTUB.
2.2.4 X-ray diffraction using synchrotron
radiation
Synchrotron facilities at HASYlab, DESY (Deutsches Electronen-Syncrotron) in
Hamburg (Germany) were used during a three-months stay in Zernike Institute for
Advanced Materials (University of Groningen, the Netherlands) in the group Solid-State
of Materials for Electronics headed by Dr. B. Noheda and Dr. T. T. M. Palstra. XRD
experiments with synchrotron radiation were assisted and supervised by Dr. C. J. M.
Daumont.
Synchrotron radiation was used with the aim of determining the B-site ordering in
(Bi,La)2NiMnO6. As explained in Sect. 1.2.5, long-range ferromagnetism is achieved,
solely, when Ni2+ and Mn4+ are ordered alternatively along [100], [010] and [001]
crystallographic perovskite directions. This B-site order produces the alternation of Niplanes and Mn-planes along [111] direction (Fig. 2.13), as a consequence of which
⎛1 1 1⎞
diffraction signal of these crystallographic planes, ⎜
⎟ superstructure double⎝2 2 2⎠
perovskite reflexion, should be recorded. Yet the structure factor of Ni and Mn are very
similar which gives rise to a very small signal, so that high intensity synchrotron
radiation was needed.
63
Chapter 2. Experimental Techniques and Data Analysis
Fig. 2.13 – B-site ordered double perovskite entails the alternation of Ni-planes and
Mn-planes along [111] crystallographic direction.
⎛1 1 1⎞
Coupled θ/2θ XRD scans around the (111) and ⎜
⎟ asymmetric reflexions (see
⎝2 2 2⎠
Sect. 2.2.1) using synchrotron radiation were performed, so that ψ and φ were set to
54.56º and 135º, respectively, in order to enable the asymmetric crystallographic planes
to diffract by keeping the condition ω = θ (see Sect. 2.2.1). The energy of synchrotron
radiation corresponded to a wavelength of 1.2651 Å.
2.3 Surface morphology
characterisation techniques
2.3.1 Field emission scanning electron
microscopy
Field emission scanning electron microscopy (FESEM) is an electronic microscope
that permits taking high resolution three-dimensional-appearance images of the surface
of samples. Alike TEM microscopes, the difference between a FESEM and a
conventional SEM is the way the electrons are produced. In FESEM a field emission
electron gun is used, whereas in conventional SEM the electrons are produced
thermoionically by heating a W or LaB6 cathode. FESEM has the advantage of
producing much smaller-diameter electron beam (< 100 Å), which leads to obtain much
higher resolution images (it can be attained spatial resolutions down to 2 nm, between 3
64
Chapter 2. Experimental Techniques and Data Analysis
and 6 times better than the resolution of a conventional SEM). In addition, since the
electron beam has a smaller diameter, the affected area of the sample is reduced. As a
consequence, samples are less electrostatically charged and the need of covering
insulating materials with conducting coatings is reduced to a large extent or even
eliminated.
The FESEM images were performed on a Hitachi S-4100-FE microscope situated in
the CCiTUB. The images were collected by using the software Quartz PCI 5.1 (Quartz
Imaging Corporation).
Figure 2.14 – Basic scheme of a typical SEM.
The SEM process is schematically depicted in Fig. 2.14. The electron beam follows
a vertical path through the column of the microscope in ultra-high vacuum, where
electromagnetic lenses focalises the beam onto the sample. The scanning coils are used
to move the electron beam on the sample. When the electron beam hits the sample, then
an interaction between the primary electrons (electron beam) and the matter takes place.
From the sample both electron and photon signals are emitted. Not all the signals are
detected and used for information. The signals most commonly used are the so-called
65
Chapter 2. Experimental Techniques and Data Analysis
secondary electrons, backscattered electrons and X-rays. The secondary electrons are
the electrons coming from atoms of the sample that have been ionised by the impact of
the primary electrons; the backscattered electrons are primary electrons that have been
elastically backscattered; and the production of X-ray is due to electron transitions of
the atoms of the sample as they have been excited on being hit by the primary electrons.
Both the secondary and the backscattered electrons are used to form the image. They are
collected and turned into a signal that is represented by a two-dimensional distribution
of intensities and it is viewed as an image by means of a cathode-ray-screen. The X-rays
give compositional information and therefore they are not used to characterise the
topography.
There are two basic modes for taking the image: by collecting the secondary
electrons or by collecting the backscattered electrons. The first ones have the advantage
of giving higher resolution images since they tend to have energies around 50 eV and
they are therefore ejected from a region very close to the surface. It is necessary to
apply a low voltage in order to collect them. The second ones might come from deeper
regions as they have higher energy. Because of this they lose surface resolution;
however, they give a better contrast as they follow rectilinear trajectories. In this work it
has been collected the secondary electrons in order to attain higher spatial resolutions.
2.3.2 Atomic force microscopy
Atomic force microscopy (AFM) is a very high-resolution type of scanning probe
microscope, with demonstrated resolutions of fractions of a nanometre. AFM provides a
true three-dimensional surface profile, which permits determining the roughness of the
sample. It works in room pressure and the samples do not need to be covered with a
conducting coating.
The AFM consists of a microscale cantilever with a sharp tip at its end that is used
to scan the sample surface. When the tip is moved close to the surface of the sample,
short-range forces (as Van der Waals) between the tip and the sample surface appear
which leads to bend the cantilever. The deflection is measured by using a laser beam
focused on the top of cantilever and reflected into an array of photodiodes, as it is
shown in Fig. 2.15. The measures within this work have been done in tapping mode, in
66
Chapter 2. Experimental Techniques and Data Analysis
which there is no contact between the tip and the sample, but the tip oscillates with a
resonance frequency. The oscillation amplitude, phase and resonance frequency are
modified because of the tip-sample interactions forces. These changes respect to an
external reference oscillation give information about the surface morphology of the
sample. A feedback mechanism is used to adjust the tip-to-sample distance in order to
maintain a constant force between them.
Figure 2.15 – Basic scheme of an AFM
AFM images were taken in a multimode force microscopy (Veeco model), which is
placed in the CCiTUB. The images were analysed with the software Nanoscope IV
(Digital Instruments). For roughness measurements of our films the root mean square
(rms) standard has been used.
2.4 Compositional
characterisation techniques
2.4.1 X-ray photoelectron spectroscopy
X-ray photoelectron spectroscopy (XPS), also known as electron spectroscopy for
chemical analysis (ESCA), is based on the photoelectron effect. It consists of irradiating
the surface of the sample by monochromatic photons (X-ray beam), producing
67
Chapter 2. Experimental Techniques and Data Analysis
excitation of the electrons of the material toward higher energy levels, or, eventually,
they may leave the solid provided that the energy of the incoming photon is sufficiently
large. The escaped electrons are detected and collected by an electron energy analyser,
which determines the kinetic energy of them. Thus, the energy of the photon, hν, is
invested: first, in extracting the electron from its binding site of the atom, EB; second, in
sending it to the vacuum, i.e. to leave the solid (work function, ϕ); and third, in
providing the electron kinetic energy. Hence, the kinetic energy, EK, is given by
EK = hν – EB – ϕ
(2.11)
Fig. 2.16 – Mn 3s photoemission spectra of (Bi0.9La0.1)2NiMnO6 thin film.
As EB is unique for each element, this technique allows determining the elements
present in the sample. Moreover, as the energy detector quantifies the number of
arriving electrons, this technique is also quantitative. However, as the mean path of the
electron through the solid is of the order of a few nm (< 10 nm), XPS is a very sensitive
surface technique.
On the other hand, the exact binding energy of an electron does not only depend on
the level from which photoemission is occurring, but the formal oxidation state of the
atom and/or the local chemical and physical environment. This can be used to determine
the valence of the elements in the sample. In particular, in the case of Mn, which was
68
Chapter 2. Experimental Techniques and Data Analysis
studied in this work, its valence state is strongly related to the Mn 3s photoelectron
spectra [9]. The spectral splitting of the 3s core-level X-ray photoemission (see Fig.
2.16) originates from the exchange coupling between the 3s holes and 3d electrons in
the transition metals. The magnitude of the splitting (≡ΔE3s) is proportional to (2S +1),
where S is the local spin of the 3d electrons in the ground state. Thus, a roughly linear
behaviour is found between ΔE3s and the formal valence of Mn (Fig. 1.17).
Fig. 2.17 – Mn 3s splitting as a function of the formal valence of Mn (from Ref. [9]).
XPS experiments were performed in a PHI 5500 Multitechnique System (Physical
Electronics) located at the CCiTUB. The system has a monochromatic X-ray source (AlKα). Multipak v6.0 (Physical Electronics) package was used as a software analysis.
2.4.2 Variable-voltage
analysis
electron
microprobe
As it was explained in SEM (Sect. 2.3.1) the impact of electrons on matter produced
the emission of X-rays. This phenomenon is used in electron microprobe analysis to
69
Chapter 2. Experimental Techniques and Data Analysis
characterise the composition of materials. In fact, the electron microprobe is usually
placed in a SEM equipment.
Fig. 2.18 – Scheme of the X-ray photon generation by the hit of an incoming electron.
The basic principle is shown in Fig. 2.18. The hit of the electrons on the matter
cause vacancies in the internal electronic levels of the atoms of the sample. The electron
transition between an external electronic level and this internal level generates an X-ray
photon, whose wavelength (or frequency) is characteristic and unique for each element.
In principle, all elements from beryllium in the periodic table can be detected by this
technique.
The X-ray photons can be determined in energy or in wavelength depending on the
detector. The technique is designated in function of the detection system: energy
dispersive spectroscopy (EDS) and wavelength dispersive spectroscopy (WDS),
respectively. Within this work it has been used a WDS detection system, which is based
on the diffraction of the X-rays through a crystal. The WDS has the advantage of having
a better resolution than the EDS.
The problem of using the electron microprobe to the compositional analysis of thin
films is the fact that the interaction volume is larger than the thickness of the film and
there is a contribution of the substrate. In order to subtract this contribution, different
electron beam energies are used so that from the different interaction volumes the
substrate contribution can be estimated and then corrected.
70
Chapter 2. Experimental Techniques and Data Analysis
WDS experiments were performed on Electron Microprobe Cameca SX50 placed at
the CCiTUB. STRATAGem (SAMx Co.) is the software that monitors the process.
2.4.3. Electron energy loss spectroscopy
Electron energy loss spectroscopy (EELS) involves measuring the energy
distribution of electrons that have crossed the sample (TEM lamella, see Sect. 2.2.3)
that have interacted with a specimen and loss energy due to inelastic scattering. The
energy loss is related to some characteristic atomic transition or solid state effect, which
is used to obtain chemical information about the sample.
A typical EELS spectrum consists of three main parts, as a function of the energy
loss. First, the zero-loss peak which represents the electrons that have not undergone
inelastic scattering, and hence they have not loosen energy. Second, the low-loss region
(from ~40 eV to ~400 eV) which consists of inelastic scattering by conduction/valence
electrons and by some inner-shell electrons. Third, the core-loss region (from ~400 eV
to ~900 eV), which consists of inelastic scattering by core electrons, typically the Ledges (2s, 2p1/2 and 2p3/2 electrons).
Whereas both the low-loss and the core-loss region are used to extract
compositional information, the latter can also be used to determine the fine structure and
the valence of the transition metals, like Mn and Ni in our case.
EELS profiles were obtained by J. M. Rebled, Dr. S. Estradé and Dr. F. Peiró in
cross section lamellas of our samples (see Sect. 2.2.3) using a Gatan GIF spectrometer
in a Jeol 2010F field emission gun TEM placed at CCiTUB.
71
Chapter 2. Experimental Techniques and Data Analysis
2.5 Functional properties
characterisation
2.5.1 Magnetic characterisation
Magnetic properties were assessed by a superconducting quantum interference
device (SQUID), which is a very sensitive magnetometer based on superconducting
loops containing Josephson junctions (insulating barrier between two superconductor
materials). The magnetic measurement is carried out by displacing the sample along the
vertical axis between two coils connected to a Josephson junction, which turns the
magnetic flux variation into voltage and transmitted as an electric signal. The Josephson
junctions permit attaining high precision, in principle, a magnetic quantum flux
(Φ0 = e/(2h) ~ 2.07·10-15 T·m2). In practise, in terms of the recorded magnetic moment
of the sample, the maximum resolution is around 10-7 emu.
Magnetic measurements were performed in a SQUID magnetometer of Quantum
Design, placed at the Institut de Ciència de Materials de Barcelona (ICMAB, CSIC).
The equipment is designed to work with magnetic fields up to 9 T and a range of
temperatures between 5 K and 300 K. Typical measurements in this work were the socalled field cool and hysteresis magnetisation. The former consists of recording the
magnetic moment response of the sample when cooling it down from room temperature
to 5 K under fix applied magnetic field (typically 1000 Oe), which enables determining
the magnetic transition temperature of the sample. The later consists of applying a
cycling magnetic field at a given temperature and recorded the magnetic moment
response, which allows obtaining the saturated magnetisation and the hysteresis loop of
the sample. It is worth mentioning that the main contribution to the measured magnetic
hysteresis loop is the diamagnetism of the substrate, which is subtracted (see Appendix
B).
72
Chapter 2. Experimental Techniques and Data Analysis
2.5.2 Electric characterisation
Dielectric measurements (see chapter 3) were mainly performed during a threemonths stay in Zernike Institute for Advanced Materials (University of Groningen, the
Netherlands) in the group Solid-State of Materials for Electronics headed by Dr. B.
Noheda and Dr. T. T. M. Palstra. Impedance analyser Agilent 4284 was used, applying,
from top to top electrode, an oscillating voltage of 50 mV of amplitude and ranging
from 40 Hz to 1 MHz. Contact with top electrodes (see chapter 3, sect. 3.1) were carried
out in a cryogenic micropositioning probe station (Janis Research Co.), see Fig. 2.19.
The probe station consist of 4 micro-manipulating dc/low-frequency (up to 40 MHz)
probe arms (Fig. 2.19), with tungsten tips (used to contact the top electrodes) that can be
moved in x, y z spatial-directions with a resolution of 5 μm inside a vacuum chamber.
Sample is mounted on a cryogenic stage (inside the vacuum chamber) that can cooled
down the sample up to ∼4.5 K using a closed-cycled liquid helium system, with a
vibration level inferior to 1 micron. An electrical resistance in the sample stage is used
to warm up the sample up to ∼420 K. On top of the probe station an optical system
consisted of a zoom lens system connected with a camera allows visualising the
displacements of the micropositioning probes on the sample in order to contact the tips
onto the electrodes. In order to avoid parasitic capacitances, coaxial cables were used
from the impedance analyser to the probe arms.
Fig. 2.19 – Cryogenic micropositioning
probe station (Janis Research Co.).
73
Chapter 2. Experimental Techniques and Data Analysis
On the other hand, magnetodielectric measurements, i.e. dielectric measurements
carried out under applied magnetic field, were performed in a Physical Properties
Measurement System (PPMS) of Quantum Design Co. placed at the Institut de Ciència
de Materials de Barcelona (ICMAB, CSIC) by Dr. I. Fina. This equipment allows a
temperature range of 4 K – 400 K and applying magnetic fields up to 9 T, while an
electric field is applied to the sample by means of the impedance analyser, in our case
LF4182 of Agilent Co. The sample is set in a sample tray with electric pins that are
connected by coaxial cables to the impedance analyser. Top electrodes connexion with
the electric pins is made by pasting tungsten wires.
Additionally, an external collaboration was established with the Dpto. Física
Aplicada III (University Complutense de Madrid), in which Dr. R. Schmidt performed
magnetodielectric measurements of our Pt/BiMnO3/Nb:SrTiO3 capacitors (see Chapter
3), using a PPMS (Quantum Design Co.) and Quadtech Impedance Analyser.
The simulation and fitting of impedance data was carried out by the commercial
software ZView.
2.5.3 Ferroelectric characterisation
A) Electric characterisation of the ferroelectric properties
Electric measurements for ferroelectric characterisation (see chapter 3) were
performed by Dr. I. Fina in a PPMS (Quantum Design Co.) placed at Institut de Ciència
de Materials de Barcelona (ICMAB, CSIC) using the commercial ferroelectric tester TF
Analyzer 2000 (AixACCT Co.) as pulse generator and current detector. Triangular
voltage pulses of typically 25 μs of rise time were used.
B) Structural characterisation of the ferroelectric properties
The ferroelectric phase transition of (Bi,La)2 NiMnO6 films was studied in
collaboration with the group headed by Dr. B. Dkhil in the Laboratoire Structures,
Propriétés et Modélisation des Solides, UMR CNRS-Ecole Centrale Paris (France). The
transition temperature was investigated by means of structural changes using
74
Chapter 2. Experimental Techniques and Data Analysis
temperature-dependent X-ray diffraction (XRD) and Raman Spectroscopy. The
experiments were performed by P. Gemeiner and Dr. B. Dkhil.
Temperature-dependent XRD
Temperature-dependent XRD measurements consist of the same procedures
explained in Sect. 2.2.1, but equipped with a sample stage which allows modifying and
stabilising the sample temperature (range 200 K to 460 K was used). A high accuracy,
two-axis diffractometer in Bragg-Brentano geometry using Cu- Kα wavelength was
used, with resolution in 2θ angle below 0.002º.
Raman Spectroscopy
Raman Spectroscopy is based on inelastic scattering of monochromatic light
(usually from a laser) when interacts with the matter. The monochromatic photons are
absorbed by the sample and then reemitted with a frequency shifted due to the
interaction with the phonons of the crystal structure. This technique is, therefore, very
sensitive to structural changes, in particular to ferroelectric phase to paraelectric phase
transitions.
Raman spectra were recorded between 80 K and 620 K with a temperature step of
20K using a T64000 triple Raman spectrometer (Jobin-Yvon-Horiba).
75
Chapter 2. Experimental Techniques and Data Analysis
References
[1] D. B. Chrisey and G. K. Hubler, Pulsed Laser Deposition of Thin Films, John Wiley
& Sons, Inc, New York, NY, 1994.
[2] R. Eason, Pulsed Laser Deposition of Thin Films, John Wiley & Sons, Inc, New
York, NY, 2007.
[3] M. Ohring, Materials Science of Thin Films: Deposition and Structure, Academic
Press, San Francisco, 2002.
[4] B. Roas, L. Schultz and G. Endres, Appl. Phys. Lett. 53 1557 (1988).
[5] D. H. Kim and H. S. Kwok, Appl. Phys. Lett. 67 1803 (1995).
[6] J. –H. Park, E. Vescovo, H. –J. Kim, C. Kwon, R. Ramesh and T. Venkatesan,
Nature 392 794 (1998).
[7] “Powder Diffraction File, version 2; Joint Comitee of Powder Diffraction
Standards” (2002), International Centre for Diffraction Data, 12, Campus Blvd, Newton
Square, Pennsylvania 19073-3273, USA.
[8] J. Als-Nielsen, D. McMorrow, Elements of Modern X-Ray Physics, John Wiley &
Sons Ltd, Chichester UK, 2011.
[9] V. R. Galakhov, M. Demeter, S. Bartkowski, M. Neumann, N. A. Ovechkina, E. Z.
Kurmaev, N. I. Lobachevskaya, Ya. M. Mukovskii, J. Mitchell, D. L. Ederer, Phys.
Rev. B 65 113102 (2002).
76
Chapter 3. Electric measurements
Chapter 3
Electric measurements
77
Chapter 3. Electric measurements
78
Chapter 3. Electric measurements
3.1 Parallel-plate capacitors
fabrication
In order to assess the dielectric and resistive properties of the multiferroic material,
i.e. in order to apply an electric field and measuring the electric response, electrodes
should be used. The easiest configuration is the so-called parallel-plate capacitors, in
which the insulating multiferroic film is inserted between two electrodes (Fig. 3.1).
Fig. 3.1 – Scheme of the process of parallel-plate capacitors fabrication.
The process of fabricating the parallel-plate capacitors in this work is explained in
the following and depicted in Fig. 3.1. Commercial conductive substrate was used as a
bottom electrode: 0.5 % Nb doped SrTiO3 (Nb:SrTiO3) as it has practically identical
structural features of non-doped insulating SrTiO3. Next the multiferroic film is grown
by PLD as described in Sect. 2.1.2. Top electrode, instead, is made ex-situ of the PLD
process chamber. A shadow mask is used, in which lines of different-diameter roundshaped holes are patterned. The mask is put into contact with the film by mechanical
pressure inside a radio frequency (RF) sputtering chamber. This deposition technique is
79
Chapter 3. Electric measurements
based on the bombardment of a target by ions of a plasma, in our case Ar plasma.
Platinum is sputtered using, typically, 3·10-3 mbar of pressure of Ar plasma with a
typical value of 20 W of power, attaining a usual thickness of 200 nm on the film. Thus,
several top electrodes are obtained on the film when the masked is removed. Typical
area of the top electrodes used in this thesis was 0.25 mm of radius (round-shaped area).
Fig. 3.2 – Scheme of electric measurements from top to top electrode in the parallelplate capacitor configuration. Ceq, A, t, ε0 and εr stand for equivalent capacitance, area
of the top electrodes, thickness, vacuum dielectric permittivity and relative permittivity
of the film, respectively.
In this geometry, the electric field is applied perpendicular to the film from top to
top electrode (Fig. 3.2), which entails measuring two identical capacitors connected in
series, each with a distance t between electrodes (which is the multiferroic film
thickness). Equivalently, it can be considered measuring one unique capacitor of
distance between electrodes of 2·t (Fig. 3.2).
Top electrodes were deposited in a RF sputtering chamber placed at the Institut de
Ciència de Materials de Barcelona (ICMAB, CSIC) by Dr. I. Fina and in a home-made
RF sputtering chamber placed at the Departament de Física Aplicada i Òptica
(University of Barcelona) in the research group Energia Solar under the supervision of
Dr. A. Antony.
80
Chapter 3. Electric measurements
3.2 Dielectric and resistive
measurements of dielectric thin
films
3.2.1 Impedance spectroscopy
When measuring the dielectric response (i.e. the capacitance) of a dielectric
material an ac voltage is required to be applied. An impedance analyser (Sect. 2.5.2)
was used as ac voltage generation and analysis of the impedance response of the
dielectric. The impedance is generally given by the modulus, |Z|, and the phase, θ, in the
complex representation: Z* = |Z|eiθ = Z’ + i Z”, where Z’ = |Z|cosθ and Z” = |Z|sinθ are
the real and the imaginary part, respectively. When perfect insulator, the multiferroic
film should behave as an ideal capacitor:
⎛ π⎞
−i
1 i⋅⎜⎝ − 2 ⎟⎠
Z =
=
e
ωC ω C
*
C
(3.1)
where C and ω stand for the capacitance of the dielectric and the angular frequency
(2πν) of the applied alternating voltage, respectively. Thus, the phase, θ, should be -90º.
Nonetheless, perfect insulators do not exist in nature, let alone multiferroics, which
tend to show poor insulating features. Hence, when an electric field is applied to the
sample, part of voltage is used to charge the capacitor, regarded as displacement current,
IDE, but some small part produces an electric current to flow through, which is called
leakage, Ileakage, as depicted in Fig. 3.3. Therefore, the impedance response of a leaky
capacitor (i.e. a multiferroic film in our case) can be modelled by a resistor, R, and a
capacitance, C, connected in parallel, in which the former accounts for the leakage,
whereas the latter accounts for the dielectric character (Fig. 3.3) [1 - 6].
81
Chapter 3. Electric measurements
Fig. 3.3 – Equivalent circuit of a leaky dielectric.
The impedance of the so-called RC-element is given by:
⎧Z R* = R
⎫
1
R
R
ω R 2C
⎪
⎪
*
=
=
−i⋅
⎨ *
1 ⎬ ⇒ Z RC = 1
1 + i ⋅ ω RC 1 + ω 2C 2 R 2
1 + ω 2C 2 R 2
⎪Z C =
⎪
ω
i
C
+
⋅
i ⋅ ωC ⎭
⎩
R
(3.2)
Note that for R → ∞, i.e. a quite insulating film, we recover expresion 3.1, i.e. Z*RC
→ Z*C and thus θ being close to -90º.
However, for typical values of the resistivity found in multiferroic materials, 106
Ω·cm, and considering a moderate/relatively large dielectric permittivity according to a
ferroelectric material, εr =125, [7 - 11], the phase, θ, of the impedance response of a 100
nm film displays a dependency on the frequency of the applied ac voltage, i.e. θ is no
longer close to –90º in the whole frequency range, as shown in the simulation of Fig.
3.4. Actually, the leaky dielectric film (RC-element) behaves as a capacitor for high
frequencies (θ ~ –90º), whereas for low frequencies it behaves as a resistor (θ ~ 0º).
This is also corroborated by the modulus of the impedance, |Z|, which acquires a
constant value at low frequencies (indicating the resistance value, R), whereas at high
frequencies it decreases at a constant logarithmic rate: Δlog|Z| ~ –Δlog|ω|, characteristic
of a capacitor. This impedance response can be demonstrated by computing the limit of
82
Chapter 3. Electric measurements
Eq. 3.2 when ω → ∞, in which expression 3.1 is obtained, and when ω → 0, in which
we obtain Z*RC → R. Hence, the impedance measured of a leaky dielectric at low
frequencies is dominated by the leakage current, Ileakage, whilst at high frequencies it is
the displacement current, IDE.
Fig. 3.4 – Simulation of the impedance response of an RC-element. The dashed line
shows the frequency dependence of |Z| (left axis), whereas the solid line shows the
frequency dependence of θ (right axis).
On the other hand, the resistivity, ρ, of insulating dielectrics shows a
semiconductor-like temperature dependence, ρ(T), thus following an Arrhenius law [8,
12, 13]:
⎛ E ⎞
ρ = ρ0 exp ⎜ a ⎟
⎝ k BT ⎠
(3.3)
where Ea and kB are the activation energy (related to the energy gap) and the
Boltzman constant, respectively. Using typical values of Ea of multiferroic materials,
0.2 eV [5, 8, 13], and applying Eq. 3.3 to the example of Fig. 3.4, a temperature
evolution of the impedance response is found as shown in the simulation plotted in Fig.
3.5. Accordingly, the resistive character of the dielectric film (i.e. θ ~ 0º) is present on
higher frequencies of the spectra on increasing temperature just due to the reducing
resistivity of the RC-element upon temperature (Eq. 3.3). Note that the capacitance was
83
Chapter 3. Electric measurements
considered temperature independent in this simulation. Thus, the frequency transition,
ωmax, between the dielectric and resistive region of the frequency spectra is shifted to
higher frequencies on decreasing the resistivity of the material, accomplishing the
relation ωmax(T)= 1/τ(T) = [R(T)·C]-1, where τ is the time constant of the equivalent
circuit representing the leaky dielectric.
Fig. 3.5 – Simulation of the frequency dependence of the impedance modulus (left) and
phase (right) of a leaky dielectric at different temperatures, T0 < T1 < T2 < T3, where
ΔT = 20 K.
It is worth mentioning, though, that few real dielectric systems can be represented
by a pure RC-element [1, 8, 14 – 18]. Most dielectrics deviate from the ideal behaviour,
including the ones studied in this thesis, showing slightly larger values than –90º of the
phase of the impedance response in the frequency spectra region where the dielectric
character contribution dominates over the resistive one. In order to account for this nonideality, the capacitance, C, is usually replaced by the so-called phenomenological
Constant Phase Element, CPE [1, 8, 15, 17, 18], whose impedance response is given by
*
Z CPE
=
1
Q ⋅ (i ⋅ ω )α
(3.4)
where Q and α (α ≤ 1, being α = 1 the ideal capacitor) denote the amplitude and the
phase of the CPE, respectively. Thus, leaky non-ideal dielectrics can be modelled by a
R-CPE element (R and CPE connected in parallel), giving the following impedance
response:
84
Chapter 3. Electric measurements
Z R* −CPE =
R
1 + RQ(i ⋅ ω )α
(3.5)
Yet Q does not have the dimension of capacitance, i.e. [F], but its units are given by
[F·s(α-1)]. Such CPE ‘capacitance’ can be converted to real capacitance, C, which is the
real dielectric response, according to the relationship C = (Q·R)(1/α)/R [8, 19 – 21]
(deduced in Appendix C).
Fig. 3.6 – Nyquist plots (–Z” vs Z’ plots) of a (a) capacitor, (b) resistor, (c) RC-element
and (d) R-CPE element.
A useful representation of the recorded impedance data consists of plotting the
negative of the imaginary part –Z” as a function of the real part Z’. In these impedance
complex planes, also known as Nyquist plots [1], a perfect insulator should depict a
85
Chapter 3. Electric measurements
vertical straight line on the –Z” axis (i.e. Z’ = 0), in which, on increasing frequency ω,
Z*C approaches to zero following Eq. 3.1 [Fig. 3.5 (a)]. Instead, a resistor should depict
a point in the Z’ axis [Fig. 3.5 (b)], which indicates the value of the resistance. Thus,
using Eq. 3.2, a dielectric material modelled by a RC-element should depict a semicircle
[Fig. 3.5 (c)], centred in the Z’ axis and of radius R/2, in which on increasing frequency,
Z*RC approaches to origin of coordinates [1 – 3, 5, 6, 8]. The angular frequency of the
applied voltage at which the semicircles shows the maximum accomplishes ωmax = 1/RC
= 1/τ [1 – 3, 5, 6, 8]. The semicircle in the Nyquist plots of a R-CPE element is slightly
depressed, i.e. no longer centred in the Z’ axis, but slightly below [Fig. 3.5 (d)], forming
an angle of (1-α)·90º with the Z’ axis [1, 8]. Note that for α = 1, the ideal case, the RC
semicircle is obtained.
3.2.2 Complex dielectric constant and ac
conductivity
In order to assess the frequency response of the dielectric properties, sometimes it is
useful to express the dielectric data in terms of the complex dielectric constant, ε* = ε’ –
i·ε”, which relates to the complex impedance by Z*=1/[i·ωε0·(A/2·t)·ε*] [1, 2, 8], where
A/(2·t) ≡ G is the geometrical factor of the measurement (Fig. 3.2). Thus, using
expression 3.2, the complex dielectric response of a leaky dielectric (modelled by a RCelement) is given by:
*
ε RC
=
−i·(1 + i·ω RC )
1
1
C
=
=
−i
*
i·ωε 0GZ RC
ωε 0GR
ε 0 G ωε 0GR
(3.6)
Therefore, unlike the impedance response shown in Eq. 3.2, in the complex
dielectric constant notation, the real part, ε’, denotes, only, the dielectric character of the
material, which can be identified as the relative dielectric permittivity [C = ε0εrA/(2·t)],
whereas the imaginary part, ε”, only shows the resistive character. Note that this is valid
for frequency spectra regions where no dielectric relaxation occurs [12, 14, 22, 23]. For
the frequency range use in this thesis (up to 1 – 2 MHz), this statement is fulfilled as
electric dipole relaxations occur at microwaves frequencies (above 300 MHz) [12, 14,
22, 23] and even at higher frequencies is the occurrence of the dielectric relaxations
related to the electronic nature of the ions [12, 14, 22, 23].
86
Chapter 3. Electric measurements
Using the same example as that shown in Fig. 3.5, thus with the same temperature
dependence of the resistivity, the simulation of the complex notation of the dielectric
constant is shown in Fig. 3.7. As a result of Eq. 3.6, ε’ remains frequency and
temperature independent (note that we have assumed the dielectric permittivity of the
material, ε = 125, temperature independent) around the associated capacitance value, C
= ε’ε0A/(2·t). However, ε”, being almost negligible in the frequency spectra region
where the dielectric contribution dominates (high frequencies), notably increases in the
frequency spectra region dominating by the resistive contribution (low frequencies).
Moreover, on increasing temperature larger values of ε” are obtained as a result of the
decreased resistivity upon temperature [ε” scales over 1/R, Eq. 3.6].
Fig. 3.7 – Simulation of the frequency dependence of the real part (left) and imaginary
part (right) of the complex dielectric constant of the leaky dielectric shown in Fig. 3.5 at
different temperatures, T0 < T1 < T2 < T3, where ΔT = 20 K.
For a non-ideal leaky dielectric (modelled by an R-CPE element), ε’ shows a small
frequency dependence (Fig. 3.8, in which α = 0.9 was considered), which follows a
–ωα-1 dependence as a result of introducing the CPE element contribution in expression
3.6:
ε
*
R − CPE
α
α +1
−i·⎡1 + RQ ( iω ) ⎤
1
⎣
⎦ = −ω α −1 Qi − i 1
=
=
ωε 0GR
ε 0G
ωε 0GR
i·ωε 0GZ R* −CPE
Note that for α = 1, expression 3.6 is obtained signalling the ideal character.
87
(3.7)
Chapter 3. Electric measurements
Fig. 3.8 – Simulation of the complex dielectric constant of non-ideal leaky dielectric
(modelled by an R-CPE element). Blue solid line shows the real part in log scale (right
axis) and the black solid line the imaginary part (left axis).
Equivalently, ε* = ε’ – i·ε” is usually replaced by the two figures of merit: the
effective capacitance [C = ε’ε0A/(2·t)], and the loss tangent or dissipation factor (tanδ =
ε”/ε’) [14].
On the other hand, when an alternating current (ac) voltage is applied, data can also
be analysed by the complex conductivity, σ* = i·ωε0ε* [8, 14, 16, 18], from the real part
of which, σ’, much information about the dielectric can be deduced. In an ideal
dielectric (characterised by an RC-element), the complex conductivity follows [14, 16,
18]:
σ* = σdc + i·ωε0ε’
(3.8)
where the real part, σ’ = σdc, corresponds to the frequency-independent direct current
(dc) conductivity, which is always present due to the leakage (related to the R of the
equivalent circuit, Fig. 3.3). Thus, the resistivity of the dielectric can be extracted by
computing ρ = 1/ σdc. However, when nonideality is taking into account, i.e. replacing
88
Chapter 3. Electric measurements
ideal capacitor C by a CPE, σ’ is no longer frequency independent [14, 16, 18] but
follows:
σ’ = σdc + σ0·ωα
(3.9)
where the frequency-dependent term, σac = σ0·ωα, showing the typical power-law
dependence on frequency, corresponds to the Jonscher’s universal dielectric response
[14, 16, 18].
Thus, by extrapolating σ’ data values toward zero frequency the resistivity of the
material can be computed (ρ = 1/σdc).
3.2.3 Extrinsic contributions to the dielectric
measurements
When performing dielectric measurements onto a sample, i.e. when applying an ac
voltage to a dielectric material, it is widely known that extrinsic electric contributions
can contribute to the total dielectric response [2 – 6, 8, 13, 16, 24 – 27]. In ceramic and
polycrystalline samples parasitic capacitance are formed at the grain boundaries as a
consequence of the different resistivity compared to that of the core of the grains.
Additionally, at the interface between the electrode and the dielectric material, a
capacitive layer, with high resistivity, tend to be formed as a consequence of the
difference between the work function of the metal and the electronic affinity of the
dielectric, causing a charge depletion/accumulation region which electrically behaves
different from the core of the material. Irrespective of the origin, due to the different
electric performance, each of these electric contributions to the total dielectric response
of the system can be considered as though they were different dielectric materials and,
hence, be modelled by an RC-element (R-CPE in non-ideal cases) [2 – 6, 8, 13, 16, 24 –
27]. For the sake of comprehension, only ideal cases will be considered in this section.
In our case, in which epitaxial thin films are obtained, the effect of the grain
boundaries is diminished to a large extent (epitaxial thin films behave as a single
crystal). Yet the electrode-film interface electric contribution cannot be neglected. Thus,
89
Chapter 3. Electric measurements
the real impedance response of the measurement is given by two RC-elements
connected in series:
Z (*RiCi ,R e Ce ) =
Ri
Re
+
1 + i ⋅ ω Ri Ci 1 + i ⋅ ω ReCe
(3.10)
where Ri and Re denote the intrinsic and extrinsic resistance, respectively, whereas Ci
and Ce denote the intrinsic and extrinsic capacitance, respectively, of the equivalent RCcircuits. In the following, the intrinsic properties, Ri and Ci, refer to the dielectric
properties of the dielectric film, while the extrinsic properties, Re and Ce, refer to the
dielectric properties of the interface capacitance.
By computing the complex dielectric constant, ε*=1/[i·ωε0GZ*], the real part, ε’, no
longer denotes the dielectric character solely as stated in expression 3.6, but follows a
much more complex expression:
ε '=
1
ε 0G ( Ri + R e )
Ri Ci + R e Ce −
Ri R e ( Ci + Ce )
R R ( C + Ce )
+ ω 2 Ri Ci R e Ce i e i
Ri + R e
Ri + R e
⎛ R R ( C + Ce ) ⎞
1+ ω ⎜ i e i
⎟
Ri + R e
⎝
⎠
2
(3.11)
2
Therefore, it is no longer valid assuming that the measured real part of the complex
dielectric response corresponds to the dielectric permittivity of the dielectric thin film.
The imaginary part follows:
ε"=
1
ε 0Gω ( Ri + Re )
1 − ω 2 Ri Ci ReCe + ω 2
Ri Re ( Ci + Ce )
( RiCi + ReCe )
Ri + Re
⎛ R R ( C + Ce ) ⎞
1+ ω2 ⎜ i e i
⎟
Ri + Re
⎝
⎠
2
(3.12)
In the following simulation, we have used the same example considered in Sect.
3.2.2, but adding an interfacial extrinsic resistance much larger than that of the film, Re
>> Ri, (as they behave as a highly resistive barriers [2, 4, 8, 16]) and an interfacial
extrinsic capacitance of 10 nF, one order of magnitude larger than that of the film. Note
90
Chapter 3. Electric measurements
that interfacial thickness is much thinner than that of the core of the film, so that
interfacial capacitance tend to be larger as inferred by the fact that the capacitance
scales over the inverse of thickness, C = εA/(2t) [4]. The frequency dependence of real
part, ε’, of the dielectric response of the total system (extrinsic + intrinsic contribution)
has been computed (Fig. 3.9). As observed, ε’ greatly differs from the behaviour of the
expected ε’ of a pure leaky dielectric (Fig. 4). In this case, ε’(ν) is separated by two
plateaus: high-frequency and low-frequency.
Fig. 3.9 – Simulation of the real part of the complex dielectric response of a leaky
dielectric film + interface electrode-film contribution.
Computing the limit when ω → ∞ and when ω → 0 in expression 3.11, it can be
deduced:
ε 'ω ↑↑ ∼
ε 'ω ↓↓ ∼
1 Ci Ce
ε 0G Ci + Ce
1
ε 0G ( Ri + Re )
2
(R C + R C )
2
i
i
2
e
(3.13)
e
thus, the dielectric permittivity extracted from the high-frequency plateau corresponds
to the equivalent capacitance of two capacitors, Ci and Ce, connected in series, i.e. the
intrinsic and extrinsic capacitance; whereas the low-frequency dielectric response is
highly altered by the interface and film resistivity.
91
Chapter 3. Electric measurements
Sometimes when analysing dielectric data, measurements are performed at one
single-frequency and the real part of the complex dielectric constant is used to evaluate
the dielectric permittivity of the material under test, using expression 3.6. This is
misleading since, even at a high frequency, there is contribution of both extrinsic and
intrinsic dielectric contributions. Only when Ce >> Ci, ε’ω↑↑ can be considered the
intrinsic dielectric permittivity of the material under test. On the other hand, only when
Ce >> Ci and/or Re >> Ri, ε’ω↓↓ signals the dielectric response of the interfacial parasitic
capacitance. Note that in the example exposed in this section Re >> Ri is accomplished.
Fig. 3.10 – Simulation of the
dielectric response of a system
formed by leaky dielectric film,
with
temperarture-dependent
resistivity,
and
electrode-film,
at
interface
different
temperatures, T0 < T1 < T2 <
T3, where ΔT = 20 K.
Assuming that the temperature dependence of the intrinsic resistivity of the
dielectric material, Ri, is given by expression Eq. 3.3, whilst considering Ci, Ce and Re
temperature independent, the temperature evolution of ε’(ν) and ε”(ν) (expressions Eq.
92
Chapter 3. Electric measurements
3.11 and 3.12) are computed (Fig. 3.10). As observed, the dielectric response clearly
resemblances to a temperature-dependent dielectric relaxation [14]. However, in this
case no proper dielectric relaxation of electric dipoles is inferred as in this simulation Ci,
i.e. the intrinsic dielectric permittivity of the material, εr = 125, is assumed temperature
and frequency independent. Hence, as a matter of fact, two electric contributions in the
dielectric response of a system (modelled by two RC-elements) can evoke an apparent
dielectric relaxation. This kind of relaxation, which is quite often reported in many
dielectric materials showing extrinsic contributions [2 – 6, 8, 13, 16, 24 – 27], is usually
referred as a Maxwell-Wagner type. Moreover, the temperature evolution of this
relaxation is driven by the temperature dependence of the resistance of either of each
RC-element.
Thus, simulations in Fig. 3.9 and 3.10 unambiguously imply that attempts to
determine the intrinsic dielectric permittivity by single fixed frequency measurements in
the presence of an extrinsic dielectric contribution may generally be doubtful, especially
at elevated temperature and/or low frequency.
Fig. 3.11 – Simulation of the impedance response of a system formed by leaky dielectric
film and an interface electrode-film. Right figure shows the high-frequency region,
zoomed from the left figure.
As each electric contribution (intrinsic dielectric material, interface capacitances,
grain boundaries, ...) will be signalled by semicircle in the Nyquist plots (Fig. 3.6), a
93
Chapter 3. Electric measurements
very useful way to determine the number of electric contributions present in the system
under test consists of plotting the measured impedance data as –Z” as a function of Z’.
In the particular case treated in this section, in which we have considered two electric
contributions (interfacial capacitance and dielectric film), computing Eq. 3.10 will give
as a result two incomplete semicircles in the impedance complex planes (Fig. 3.11).
Note that as we have assumed Re >> Ri, low-frequency semicircle is much larger than
that of high-frequency. As a consequence the high-frequency semicircle is only able to
be observed by zooming the high frequency region of the Nyquist plot (Fig. 3.11 right).
It is also worth mentioning that the experimental set up may also contribute to the
impedance response of the measurement. This contribution consists, basically, of the
resistance of the measurement probes and cables and the inductance of the cables. The
former can be accounted by adding a single resistor, R0, in series to the equivalent
circuit of the system, whereas the latter can be accounted by adding a single inductance
element, L0, in series [8].
Fig. 3.12 – Effect of the inductance of the experimental set up in the frequency response
of the impedance of a system formed by a leaky dielectric film and an interface
capacitance. The blue solid line signals the phase of the impedance, whereas the black
solid line the modulus of the impedance.
It is worth noting that inductance of cables may have a significant contribution at
high frequencies (as ZL = i·ωL), which can mask the high frequency dielectric data and
thus giving rise to misleading interpretation of the results. In our experimental set up L0
94
Chapter 3. Electric measurements
was found to be ~10-6 H. Adding this L0 value to the system of interface capacitance
and dielectric film, the impedance response is given in Fig. 3.12. As observed, at low
frequencies and intermediate-high frequencies the phase of the complex impedance is
close to -90º, signalling Ce and the equivalent capacitance of Ce and Ci in series,
respectively. These two frequencies regimes are separated by a phase peak, indicating
the Maxwell-Wagner relaxation. However, at the highest frequencies, the phase is
rapidly increasing toward +90º, pointing out that the inductance is completely
dominating the frequency spectra of the impedance data. This fact limits, to a large
extent, extracting the intrinsic dielectric properties at high frequencies.
3.2.4 Magnetocapacitance measurements.
As stated in Sect. 1.1.3, one indirect consequence of the coupling between the
magnetic and the ferroelectric order is the magnetic dependence, H, of the dielectric
permittivity, ε. This fact has promoted a flurry of research based on magnetocapacitance
measurements, i.e. measuring ε under different H, of possible candidates to display
magnetoelectric coupling such us multiferroics or nanocomposites formed by
ferroelectric and magnetic materials [10, 28 – 36]. Magnetocapacitance data is usually
shown as a relative change of the dielectric permittivity, i.e. MC = [ε(H)- ε(0)]/ε(0)].
It is clear, though, that having a Maxwell-Wagner relaxation, as described in Sect.
3.2.3, magnetocapacitance can also be arisen from changes in the resistivity as long as
the resistivity displays magnetic-field dependence (Eq. 3.11). Hence, and important to
be noted, magnetocapacitance alone is not a sufficient criterion to signal the occurrence
of the coupling between the ferroelectric and magnetic order [4, 35, 37].
For the sake of example, let’s assume that the resistivity of the dielectric film of the
example exposed in Sect. 3.2.3 decreases on increasing H (i.e. displaying negative
magnetoresistance), following the relation ρ(H) ~ ρ(0)exp(-H/H0), where H0 is a scaling
parameter. Note that this expression is found in well known magnetoresistive materials
like (La,Ca)MnO3 [38]. Assuming H0 = 20 kOe [38], Fig. 3.13 shows the frequency
dependence of the complex dielectric response of the system formed by an interface
capacitance and a dielectric film (Sect. 3.2.3).
95
Chapter 3. Electric measurements
Fig. 3.13 – Simulation of the frequency dependence of the dielectric response of a
system formed by leaky dielectric film, with magnetic-field-dependent resistivity, and
interface electrode-film, at different magnetic fields.
Therefore, according to the simulation shown in Fig. 3.13, measuring the magneticfield dependence of ε’ at one-single frequency will give rise to a positive
magnetocapacitance effect, yet not due to a multiferroic coupling but because of the
negative magnetoresistance. Note that irrespective of the relation that follows the
magnetoresistance (the expression used above does not have to apply for all materials),
a negative magnetoresistance would produce a positive magnetocapacitance effect and,
conversely, a positive magnetoresistance would produce a negative magnetocapacitance
effect, as long as a Maxwell-Wagner relaxation occurs.
96
Chapter 3. Electric measurements
A useful way to disentangle magnetoresistive effects from genuine magnetoelectric
coupling consist of performing the aforementioned impedance spectroscopy, by means
of which, not only the extrinsic dielectric contributions can be determined and
consequently ruled out, but also allows deconvoluting the resistive and dielectric
character of the dielectric material that is under test.
3.3 Electric characterisation of
the ferroelectric properties
The common electric characterisation of the ferroelectric properties consists of
recording the polarisation, P, on cycling (Fig. 3.14) an applied electric field, E, i.e. the
ferroelectric hysteresis loop.
Fig. 3.14 – Applied triangular voltage signal in a
ferroelectric hysteresis loop.
Nonetheless, what is measured on applying voltage is not the polarisation itself, but
the current, I. The polarisation is computed by P = Q/A where A is the area of the top
electrodes and Q is the measured charge, which is obtained by integrating the measured
current over time during the cycle:
Q = ∫ I (t )dt
(3.14)
In an ideal condition, i.e. a perfect insulator, the measured current should
correspond to the displacement current, IDE (Fig. 3.3), which, in a ferroelectric, basically
consists of the charging current of the capacitor, Iε, and the current related to the
ferroelectric domain switching, IFE, i.e. IDE = Iε + IFE. Note that Iε, arisen from the
97
Chapter 3. Electric measurements
induced polarisation, is responsible for the characteristic non-saturated hysteresis loops
in ferroelectrics [39].
However, as pointed out in previous sections, as leakage is present in any dielectric
(Fig. 3.3), the current related to the conductive part of the sample, Ileakage, is also
recorded in the measurement, so that the integrated charge is given by:
Q = ∫ I DE (t )dt + ∫ I leakage (t )dt
(3.15)
This is one of the main sources of measuring apparent ferroelectric hysteresis loops
in non-ferroelectric materials [39 – 41], as described on the following.
Fig. 3.15 – Charge as a function of the applied voltage for a resistor (red solid line), a
linear dielectric (blue solid line) and a leaky linear dielectric (green dashed-dotted
line).
Considering a pure resistor, Ileakage will be proportional to the applied voltage (I =
V/R), and thus, also to time as we are applying a triangular signal. Then it follows:
Qleakage = ∫ I leakage (t )dt ∼ t 2 + K ∼ V 2 + K '
(3.16)
(where K and K’ are integration constants) i.e. Qleakage(V) will show two parabolas (Fig.
3.15, red solid line), whose concavity is different for the negative and positive slopes of
98
Chapter 3. Electric measurements
the voltage signal, giving rise to the characteristic ‘rugby-shape’ form. Note that the
charge at the beginning and at the end of the voltage cycle is not zero. This is due to the
algorithm used in the software of the ferroelectric testers that positions the curve
symmetrically to the polarisation values (or, equivalently, charge values). The
recollected Qleakage will increase on increasing the period of the cycle. Conversely,
considering a pure linear dielectric, C, (with no ferroelectric order), the charge will be
proportional to the applied voltage (Qε = CV), i.e. the slope will indicate the capacitance
(or, equivalently, the dielectric permittivity) of the dielectric (Fig. 3.15, blue solid line).
Hence, it is clear that a leaky linear dielectric (Qε + Qleakage) will produce a closed Q(V)
loop, resembling a ferroelectric hysteresis loop (Fig. 3.15, green dashed-dotted line).
This loop will be increasingly open on increasing the measuring time, i.e. the period of
the cycle, as Qleakage will increase, contrarily to real ferroelectric hysteresis loop, in
which the coercive electric field decreases on increasing the measuring time [39].
Fig. 3.16 – Schematic representation of a PUND measurement.
In order to avoid parasitic contributions, Qleakage, to the measured ferroelectric
hysteresis loop, the so-called positive-up-negative-down (PUND) technique [42 – 44]
tend to be used. PUND technique consists of 5 voltage pulses (Fig. 3.16), in which the
current is simultaneously recorded (except for the first pulse). The first one, labelled as
‘pre-poling’, is negative and serves to polarise the sample to –P. The current recorded
during the second pulse, which is positive, labelled as P, contains all the contributions:
Iε, IFE and Ileakage. Instead, the current recorder in the third pulse, labelled as U, only
contains Iε and Ileakage, as U is also positive and the sample is already polarised, +P (i.e.
no current is recorded for the ferroelectric domain switching). Using the same
arguments, the current recorded in the pulses N and D, IN and ID, respectively, follows
IN = Iε + IFE + Ileakage and ID = Iε + Ileakage. Thus, by subtracting the current resulting from
99
Chapter 3. Electric measurements
the U pulse from that of the P pulse (and similarly D from N) we only obtain the current
related to the switching of the ferroelectric domains, IFE.
Thus, by integrating IFE over the measuring time (Eq. 3.14) we obtain the
ferroelectric hysteresis loop, P(E). Note that the ferroelectric hysteresis loops computed
from PUND measurements are rectangular-shaped (i.e. saturated), as not only Ileakage is
suppressed, but also Iε. Therefore, this technique directly gives the remanent
polarisation values.
It is worth recalling that for the ferroelectric hysteresis loops, the parallel-plate
capacitors configuration was used [see Sect. 3.1]. Thus, it follows that E = V/(2·t),
where V is the applied voltage from top to top electrode and t is the film thickness.
100
Chapter 3. Electric measurements
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103
Chapter 3. Electric measurements
104
Chapter 4. BiMnO3 thin films
Chapter 4
BiMnO3 thin films
105
Chapter 4. BiMnO3 thin films
106
Chapter 4. BiMnO3 thin films
4.1 Single-phase stabilisation
The stabilisation of single phase Bi-based manganite-family perovskites has been,
in general, difficult to achieve because of their tendency of multiphase formation and
the high volatility of bismuth [1 – 4]. Indeed, BiMnO3 in bulk form is only achieved in
extreme sintering conditions, i.e. between 3 and 6 GPa and between 600 ºC and 700ºC
of mechanical pressure and temperature, respectively [5 – 9]. Heating at ambient
pressure a mixture of bismuth oxide and manganese oxide leads to the formation of
Bi12MnO20 and Bi2Mn4O10 compounds, much more stable than the perovskite BiMnO3
[9].
Still, as explained in Sect. 1.3, metastable compounds can be formed by replacing
the mechanical pressure by the epitaxial stress, i.e. using substrates with similar
structures and whose lattice parameters show a low mismatch with those of the
compound that is to be formed. Here, the perovskite oxide SrTiO3 was used as a
substrate, whose crystal structure is cubic (a = 3.905 Å). The small lattice mismatch
(table 4.1) with regard to a and c BiMnO3 lattice parameter (pseudo-cubic
representation: a ≈ c ≈ 3.935 Å, b ≈ 3.989 Å, α ≈ γ ≈ 91.46º, β ≈ 90.96º [5]) evidences
the suitability of SrTiO3 substrate for the epitaxial stress needed to synthesise the
compound.
Substrate
Structure
and
orientation
Lattice
parameter
(Å)
SrTiO3
Cubic
perovskite
(001)
3.905
Mismatch Mismatch Mismatch
with a
with b
with c
parameter parameter parameter
of BiMnO3 of BiMnO3 of BiMnO3
0.77%
2.15%
0.77%
Table 4.1 – In-plane lattice parameter and orientation of the substrate and mismatch
⎛ a (b, c) BiMnO3 − aSrTiO3
⎜
⎜
aSrTiO3
⎝
⎞
⎟ with the lattice parameters of BiMnO3.
⎟
⎠
BiMnO3 thin films were grown by PLD (Sect. 2.1) from non-stoichiometric targets,
i.e. the mixture containing Bi/Mn oxides was 10% atomically Bi-rich in order to
compensate for the Bi volatility. According to the mismatch with SrTiO3 substrate
107
Chapter 4. BiMnO3 thin films
(table 4.1), BiMnO3 thin films are expected to grow (010)-oriented, i.e. with the b-axis
as the out-of-plane direction, as b parameter shows the largest mismatch. Thus, only
(0k0) reflexions of BiMnO3 are to be found in the symmetric θ/2θ XRD diffractograms.
In order to optimise the deposition conditions for the single-phase stabilisation, the
substrate temperature and the oxygen pressure during the growth process were assessed
as well as the role of the thickness.
4.1.1 Dependence on temperature
By keeping the rest of the PLD deposition conditions fixed (see Sect. 2.1), we grow
different samples at different substrate temperatures, ranging from 590ºC to 700ºC.
In Fig. 4.1, XRD θ/2θ scans of 50-nm thick films grown at 0.1 mbar at various
illustrative temperatures are shown. The (0k0) reflections of the BiMnO3 phase can be
clearly observed, which take place at 2θ values slightly smaller than the (00l) reflexions
of SrTiO3, as expected since b lattice parameter of BiMnO3 is larger than that of SrTiO3
[note that, having in mind the Bragg diffracion law (Eq. 2.1), the interplanar distance of
the (0k0) reflexions, d0k0 = b/k (Appendix XRD), is larger in the case of BiMnO3 films].
The lattice parameters will be assessed in sect. 4.2.2.
However, in addition to the (0k0) reflexions of BiMnO3, the diffractograms reveal
the presence of other phases of the Bi – Mn – O ternary system (Fig. 4.1). Importantly
enough, a correlation between these parasitic phases and the substrate temperature is
observed. In the samples prepared at lower temperatures than 630ºC, Bi-rich phases,
such as Bi2O3 and Bi12MnO20 coexist with BiMnO3. The presence of these phases is
monotonously reduced on increasing temperature and eventually disappearing at around
630ºC. Conversely, in the samples prepared at temperatures higher than 630ºC, it is the
Mn-rich phases, such as Mn3O4 and Bi2 Mn4O10, the ones that coexists with BiMnO3
phase. Moreover, the presence of these Mn-rich phases is enhanced on increasing
temperature. It is only the XRD patterns of the films prepared at the intermediate
temperatures around 630ºC which displays the (0k0) reflexions of BiMnO3 without
traces of spurious phases.
108
Chapter 4. BiMnO3 thin films
Fig. 4.1 – (a) XRD θ/2θ scans of BiMnO3 thin films (50 nm thick) grown at 0.1 mbar of
O2 and at different temperatures. (x) denotes the (0k0) reflexions of BiMnO3 phase.
Parasitic phases belonging to the Bi – Mn – O system are signalled by capital letters:
(A) Mn3O4; (B) Bi2Mn4O10; (C) Bi12MnO20; (D) Bi2O3. (b) Zoom of the (001) reflexion
of SrTiO3 and (010) reflexion of BiMnO3.
On the other hand, as observed in Fig. 4.1 (b), the (0k0) reflexions of BiMnO3 shifts
toward higher 2θ values on increasing temperature above 630ºC. Hence, according to
the Bragg’s law (Eq. 2.1), the interplanar distance of the (0k0) reflexions, d0k0, is
reduced at higher temperatures and consequently the out-of-plane lattice parameter, b
(Appendix XRD), as shown in Fig. 4.2. Considering that the in-plane lattice parameter
109
Chapter 4. BiMnO3 thin films
of BiMnO3 is fully strained on SrTiO3, as will be inferred in Sect. 4.2.2, and hence it
adopts the SrTiO3 lattice parameter, the unit cell volume is monotonously reduced at
high temperatures (right axis), signalling a change in the film composition. A variation
of the oxygen concentration is possible, but the presence of anion vacancies is known to
produce an enlargement of the unit cell volume [10 – 12]. Conversely, cation vacancies
produce a reduction of the unit cell volume, as proved in either LaMnO3 [13] or
BiMnO3 [3]. Taking into account the high Bi volatility compared to Mn, it is reasonable
to argue that this unit cell volume reduction at high temperatures is driven by the
presence of Bi vacancies.
Fig. 4.2 – Evolution of the lattice parameter (left axis) and unit cell volume (right axis)
of BiMnO3 as a function of the deposition temperature. In computing the unit cell
volume the in-plane lattice parameter of BiMnO3 is assumed to be coincident with that
of SrTiO3 (see Sect. 4.2), thus assuming a tetragonal unit cell for BiMnO3.
Thus, XRD results suggest that the Bi-content in the films decreases on increasing
the deposition temperature (substrate temperature), in agreement with the high volatility
of this element. In order to bear out this tendency, the chemical composition of the films
prepared at different temperatures was assessed by X-ray wavelength dispersive
spectroscopy technique (described in Sect. 2.4.2). The results can be summarised in
Fig. 4.3, in which the evolution of the [Bi]/[Mn] atomic ratio as a function of the
deposition temperature is depicted. As observed, there is a slight monotonic reduction
110
Chapter 4. BiMnO3 thin films
of the Bi content when the deposition temperature varies from 600ºC to 630ºC, in
agreement with a slightly increase of the Bi desorption rate upon temperature. However,
above 630ºC Bi amount is severely reduced, attaining 50 % of the nominal value at
645ºC and 25% at 660ºC. This finding evidences a substantial change in the Bi
desorption rate (i.e. a strong increase) during growth occurring when depositing at
higher temperatures than 630ºC, giving rise to largely Bi-deficient samples. Very
similar behaviour was found, indeed, for the Bi-content in columnar nanocomposites
BiFeO3-CoFe2O4 [14].
Fig. 4.3 – Cationic composition ratio, [Bi]/[Mn], of Bi – Mn – O films as a function of
the deposition temperature. Data are subjected to a 10% of experimental error.
Thus, as expected, the appearance of Mn-rich phases in the XRD patterns of the
samples prepared at high temperatures (Fig. 4.1) is promoted by the large Bi loss in Bi –
Mn – O system. However, the samples prepared at low temperatures do not show an
excess of Bi-content, as expected for the appearance of Bi-rich phases, but shows
[Bi]/[Mn] ratio slightly below the nominal value 1:1 (Fig. 4.3). The Bi – Mn – O
multiphase formation at low temperatures is likely caused by the incomplete reaction or
low mobility of the arriving species (Bi and Mn oxides) at the substrate surface to form
BiMnO3. The temperature dependence of the reaction rate, r, tend to follow an
Arrhenius law, i.e. r ~ exp(-Ea/kBT) [4], where Ea is the activation energy of the reaction
and kB is the Boltzman constant. Ea depends on the reaction. Hence, in order to achieve
111
Chapter 4. BiMnO3 thin films
a complete reaction of the Bi and Mn oxides to form BiMnO3, overcoming the more
stable phases Bi2O3 and Bi12MnO20, it is necessary to increase the thermal energy kBT.
However, the Bi desorption rate from the substrate surface also increases on increasing
temperature following rdes ~ exp(-Edes/kBT) [4], where Edes is the activation energy of the
desorption process (which is very small for volatile elements like Bi as inferred from
Fig. 4.3) [4]. The high desorption rate is responsible for the highly Bi-deficient samples
prepared at high temperatures and consequently the formation of Mn-rich phases. As a
result, obtaining single phase BiMnO3 in the Bi – Mn – O system is a very delicate
balance between the reaction rate of the arriving species and the Bi desorption rate,
leading to a very narrow window of deposition temperatures in which it is achieved
(around 630ºC in our case). It is worth mentioning, though, that this narrow window of
deposition temperatures in which single phase BiMnO3 is obtained is not an universal
recipe as it may greatly differ or even disappear depending on the target composition
(i.e. the Bi:Mn ratio in the target), the deposition rate (the higher the lower Bidesorption due to the shorter time of the growth process), the laser ablation fluency, ...
4.1.2 Dependence on O2 pressure
By keeping the rest of the PLD deposition conditions fixed (see Sect. 2.1), we grow
different samples at 630ºC for different O2 pressures inside the chamber, ranging from
vacuum to 0.3 mbar.
In Fig. 4.4, XRD θ/2θ scans of 50-nm thick films grown at 630ºC under various
illustrative oxygen pressures are shown. The (0k0) reflections of the BiMnO3 phase can
be clearly observed in all the oxygen pressure range except for the sample prepared in
vacuum, in which BiMnO3 compound is not formed. This latter is likely due to a large
oxygen deficiency, evidencing the requirement of using partial oxygen pressures when
growing complex oxides. Moreover, in the XRD patterns of the films prepared in
vacuum traces of Mn3O4 phase appear, similar to what is found for samples prepared at
high temperatures (Fig. 4.1), which signals a similar Bi-deficiency but driven in this
case by heating in vacuum conditions.
112
Chapter 4. BiMnO3 thin films
Fig. 4.4 – XRD θ/2θ scans of BiMnO3 thin films (50 nm thick) grown at 630ºC and at
different O2 pressures. (x) denotes the (0k0) reflexions of BiMnO3 phase. Parasitic
phases belonging to the Bi – Mn – O system are signalled by capital letters: (A) Mn3O4;
(B) MnO2; (C) Bi2O3.
For the samples prepared in the range of O2 pressures comprised between 0.05 and
0.1 mbar, single phase BiMnO3 thin films are obtained. Yet when further increasing the
partial oxygen pressure in the deposition process, XRD patterns show additional
113
Chapter 4. BiMnO3 thin films
reflexions corresponding to parasitic phases (Fig. 4.4). This fact reveals the pronounced
multiphase character of the Bi – Mn – O system. It is worth noting that the presence of
MnO2 phase, which corresponds to Mn4+ of oxidation state, is increasingly enhanced
upon O2 pressure. An over-oxidation of the films will produce an increase of the
valence state of the transition metals, i.e. from Mn3+ (the appropriate oxidation state for
BiMnO3 compound) to Mn4+, in order to maintain the electric equilibrium. According to
XRD results (Fig. 4.4), an over-oxidation of Bi – Mn – O system seems to lead to phase
segregation, i.e. the formation of Mn4+-phases with the excess of Mn4+, rather than
producing single-phase BiMnO3 containing multivalent Mn3+/Mn4+ at the B-site.
Additionally, the samples prepared at the highest oxygen pressure (0.3 mbar), Bi2O3
phase is also detected in the XRD patterns (Fig. 4.4), which might be the result of a
smaller Bi desorption rate due to the higher pressure inside the chamber. Similar Bi-rich
phases were detected either at low deposition temperature or at high oxygen pressure
when growing BiFeO3 films due to a larger [Bi]/[Fe] cationic ratio in either case [15].
Fig. 4.5 – Phase diagram of Bi – Mn – O films grown on (001)-oriented SrTiO3 as a
function of the deposition temperature and the oxygen pressure during the growth
process. The green solid line signals the window of deposition conditions in which
single-phase BiMnO3 is achieved.
As a summary, from the XRD results a partial phase diagram of Bi – Mn – O films
can be deduced as a function of the deposition temperature and oxygen pressure during
the growth process, which is shown in Fig. 4.5. As observed, either at low high
114
Chapter 4. BiMnO3 thin films
temperatures or at high pressures, Bi-rich phases appear together with the BiMnO3
phase. Conversely, the films prepared either at high temperatures or low oxygen
pressure show Mn-rich phases consistent with a larger Bi-deficiency. Thus, only in a
narrow window of deposition conditions (marked by a green solid line in Fig. 4.5)
single-phase BiMnO3
is achieved. Yet, as aforementioned, different target
stoichiometry, laser fluence, etc may modify this narrow window and the phase diagram
of Bi – Mn – O system.
4.1.3 Dependence on thickness
In this section we have investigated the influence of the thickness of Bi – Mn – O
films on the single-phase stabilisation of BiMnO3 phase. The samples that have been
studied correspond to those grown in the narrow deposition conditions determined in
Sect. 4.2.1 and 4.2.2, in which single-phase BiMnO3 is achieved in 50-nm thick films,
i.e. at 630ºC and 0.1 mbar of O2 pressure.
In Fig. 4.6 XRD θ/2θ scans of three illustrative samples of different thickness, i.e.
30, 60 and 100 nm are plotted. As observed, the thickest film displays a clear
multiphase character, despite being grown at the narrow window of deposition
conditions for the single-phase stabilisation (see Sect. 4.21 and 4.2.2). This multiphase
tendency upon thickness could be due to a kind of mechanism of strain relaxation,
instead of the common one which would consist of BiMnO3 film lattice parameters
becoming closer to those of the bulk upon thickness [16]. However, as a matter of fact,
the parasitic phases that arise in the thickest films are all Mn-rich, i.e. Mn3O4 and
Bi2Mn4O10, similar to what is found in thinner Bi – Mn – O films grown at high
temperatures (Sect. 4.2.1). This fact points out to the possibility of an increasing Bideficiency upon thickness.
115
Chapter 4. BiMnO3 thin films
Fig. 4.6 – XRD θ/2θ scans of Bi – Mn – O thin films (different thickness) grown at
630ºC and at 0.1 mbar of O2 pressure. (x) denotes the (0k0) reflexions of BiMnO3
phase. Parasitic phases belonging to the Bi – Mn – O system are signalled by capital
letters: (A) Mn3O4; (B) Bi2Mn4O10.
In order to further study this possibility, thick films (90 nm – 120 nm) of Bi – Mn –
O system were grown at different temperatures (at 0.1 mbar of O2 pressure). The XRD
θ/2θ scans of some illustrative samples are shown in Fig. 4.7. The results show a
multiphase tendency regardless the deposition temperature. Still, interesting enough, the
spurious phases are all Mn-rich, even for the samples prepared at low temperatures
(note that 50-nm thick Bi – Mn – O films deposited at 600ºC and 615ºC display Bi-rich
phases, as shown in Fig. 4.1). Nonetheless, it is worth noting that the presence of
116
Chapter 4. BiMnO3 thin films
Bi2Mn4O10 phase is larger than Mn3O4 phase the lower the deposition temperature is, in
agreement with an increasing Mn enrichment of Bi – Mn – O films upon temperature as
deduced in Sect. 4.2.1.
Fig. 4.7 – XRD θ/2θ scans of Bi – Mn – O thin films (90 – 110 nm) grown at 0.1 mbar of
O2 pressure and at different temperatures. (x) denotes the (0k0) reflexions of BiMnO3
phase. Parasitic phases belonging to the Bi – Mn – O system are signalled by capital
letters: (A) Mn3O4; (B) Bi2Mn4O10. (*) denotes the Kβ of (002) SrTiO3.
Hence, according to the XRD results, the Bi – Mn – O films seem to be increasingly
Bi-deficient the thicker they are, irrespective of the deposition temperature. Chemical
analysis of the samples of different thickness was carried out by X-ray wavelength
117
Chapter 4. BiMnO3 thin films
spectroscopy, the results of which are summarised in Fig. 4.8. As observed the
[Bi]/[Mn] cationic ratio of Bi – Mn – O films is strongly reduced on increasing
thickness, proving the fact that the thicker the film the larger the Bi-deficiency. Thus, it
might indicate that the Bi desorption rate, rdes, is higher than the incoming Bi ablated
material, even for low deposition temperatures [rdes increases upon temperature, ~exp(Edes/kBT)]. Consequently, this deviation would be increasingly emphasised the longer
the deposition time, i.e. the thicker the films (note that the pulsed laser repetition rate
was maintained constant at 5 Hz, sect. 2.1), leading to increasingly Mn-rich films upon
thickness.
Fig. 4.8 – Cationic composition ratio, [Bi]/[Mn], of Bi – Mn – O films grown at 630ºC
and at 0.1 mbar of O2 pressure as a function of film thickness. Data are subjected to a
10% of experimental error.
Still, another plausible possibility is the fact that the ablated material from the target
might be increasingly Bi-deficient during the growth process, as it would produce
similar off-stoichiometric films as shown in Fig. 4.8. The laser-matter interaction
produces local high temperatures, vaporising the volatile elements, i.e. Bi, from the
target surface affected by the laser. Thus, the reiteration of the laser pulses onto the
target surface will make it increasingly Mn-rich pulse after pulse, and hence the ablated
material will become increasingly Bi-deficient on increasing the deposition time. In
order to corroborate this argument, the composition of the surface of the target was also
118
Chapter 4. BiMnO3 thin films
assessed by X-ray wavelength spectroscopy, but analysing two different areas: a region
that has been hit by the laser after deposition and another one that has not. The results
(Table 4.2) show clear differences, i.e. whereas the region that is not altered by the laser
displays a [Bi]/[Mn] cationic ratio close to the nominal composition of the target, that
region that has been altered by the laser pulses (5000 pulses, ~ 100 nm) present clear
Bi-deficiency (~ 50% of the nominal value).
Surface target
composition
Nominal
Region non-altered
by the laser
Region altered by
the laser
[Bi]/[Mn] ratio
1.10
1.07
0.55
Table 4.2 – [Bi]/[Mn] ratio of the target surface. Data are subjected to a 10% of
experimental error.
Thus, according to the composition results, the stoichiometry of the surface target is
not preserved after the laser interaction, becoming increasingly Bi-deficient the longer
the exposition time. Additionally, long deposition time leads to large Bi-desorption
from the growing film and therefore increasingly Bi-deficient. Hence, the increasingly
Bi-deficient Bi – Mn – O films upon thickness can be explained by a combination of
these two factors: the increasingly Bi-deficient ablated material and the increasing Bi
desorption from the growing film upon deposition time. In this sense the 2D phase
diagram shown in Fig. 4.5 becomes quite much complicated as another variable
(deposition time) should also be accounted.
4.2 Structural characterisation
and surface topography
4.2.1 Texture of the films
First assessment of the crystal structure was focused on the dispersion of the out-ofplane lattice parameter of the film from the growth direction. As explained in Sec. 2.2.1,
a way to quantify the so-called out-of-plane texture is by means of the FWHM of the
119
Chapter 4. BiMnO3 thin films
rocking curves (ω scans). In this work we have performed the rocking curves around the
(001) Bragg reflexion [(010) in the case of BiMnO3]. This figure of merit is compared
with that of the substrate, as being the latter a single crystal with presumable high
quality and free from form factor effects. Thus, the FWHM of the substrate Bragg
reflexion may represent the estimate width to be achieved in a film for the instrumental
width.
Fig. 4.9 – Rocking curve of the (001) reflexion of SrTiO3 substrate and 50-nm BiMnO3
film grown at 630ºC and 0.1 mbar of O2 pressure.
Rocking curves of the (010) BiMnO3 and (001) SrTiO3 Bragg reflexions are
illustrated in Fig. 4.9 of a 50-nm BiMnO3 film grown in the optimised deposition
conditions for single-phase formation. Comparison of the rocking curves reveals that
the FWMH value of the BiMnO3 peak (0.24º) is of the order of that of the substrate
(0.15º), though substantially larger, which indicates a certain out-of-plane dispersion of
the BiMnO3 unit cells. The FWHM ratio between the rocking curve of BiMnO3 and that
of the substrate (~1.5) is extensive for the rest of the films up to 70 nm of thickness.
In-plane texture, i.e. how BiMnO3 unit cells are in-plane oriented, is characterised
by ϕ-scans of an asymmetric reflexion (see Sect. 2.2.1), which allows planes that are not
parallel to the interface to diffract. When it comes to choosing an appropriate
asymmetric reflexion, the criterion is based on using an easy in-plane axis, such as the
[100] or [010] SrTiO3 directions, which are equivalent as being a cubic structure.
120
Chapter 4. BiMnO3 thin films
However, due to the similarity of the lattice parameters of both SrTiO3 and BiMnO3,
which means similar 2θ angle of the Bragg reflexions, a high-2θ reflexion was required
in order to minimise the substrate contribution to the ϕ-scans of the film, since
difference in 2θ is larger the higher the angle is. Thus, (103) reflexion [(130) in the case
of BiMnO3] was used, whose difference in 2θ between BiMnO3 and SrTiO3 is about
1.8º (see table 4.3).
XRD reflexion
2θ(º)
ω(º)
ψ(º)
(103) SrTiO3
77.2
38.6
18.4
(130) BiMnO3
75.4
37.7
18.2
Table 4.3 – Four-circle diffractometer angles at which the (103) reflexion of SrTiO3
and (130) reflexion of BiMnO3 take place. ϕ angle is four times degenerated and 90º
separated when tetragonal (cubic) in-plane crystal symmetry.
Fig. 4.10 depicts the XRD ϕ-scans of the asymmetric (103) reflexion of substrate
and (130) reflexion of BiMnO3 film (50 nm thick) grown in the optimised deposition
conditions for single-phase formation. As shown, only four 90º-ϕ-spaced peaks of the
film are observed, which not only indicates that there are no contributions of
misoriented in-plane family of crystallites of BiMnO3, i.e. BiMnO3 films are in-plane
textured, but also that the crystal symmetry of BiMnO3 films corresponds to that which
allows an orthogonal in-plane unit cell base, i.e. orthorhombic, tetragonal or cubic.
Moreover, the fact that BiMnO3 ϕ peaks coincide in ϕ angle value with those of the
substrate (Fig. 4.10) proves that BiMnO3 films have grown cube-on-cube, i.e. the
tetragonal base is coincident in orientation with that of the cubic substrate (see Sect.
2.2.1). Or, in other words, the [100] in-plane crystallographic direction of BiMnO3 film
is parallel to the [100] direction of SrTiO3, which is normally represented by the
epitaxial relationship [100]BiMnO3(010)//[100]SrTiO3(001). The cube-on-cube growth
is confirmed along thickness up to 70 nm.
121
Chapter 4. BiMnO3 thin films
Fig. 4.10 – XRD ϕ-scans around the (130) reflexion of BiMnO3 film, 50-nm thick, grown
at 630ºC and 0.1 mbar of O2 and (103) reflexion of SrTiO3 substrate.
4.2.2 Reciprocal space maps and lattice
parameters
Reciprocal space maps (RSM) consists of plotting the out-of-plane component,
qperp, of the reciprocal space vector, q hkl , of the (hkl) XRD reflexion versus the in-plane
component, qparallel. They have been performed in order to determine the film lattice
parameters (both the out-of-plane and in-plane lattice parameters, as long as an
122
Chapter 4. BiMnO3 thin films
asymmetric XRD reflexion is assessed) and the epitaxial strain of BiMnO3 films (see
Sect. 2.2.1). In the reciprocal space map, not only the film XRD reflexion is recorded
but also that of the substrate, as the (qparallel, qperp) XRD peak position of the film
compared to that of the substrate is used to evaluate the strain and extract the correct
lattice parameters of BiMnO3 films by accounting the instrumental error, as discussed in
Appendix C.
Fig. 4.11 – Reciprocal space of the allowed XRD reflexions in the 4-circle
diffractometer for both BiMnO3 (solid circles) and SrTiO3 (solid squares), when [100]
and [001] ([010] for BiMnO3) crystallographic directions are the in-plane and out-ofplane directions, respectively. Top and right axis indicates the corresponding in-plane
and out-of-plane reciprocal lattice units of the XRD reflexions, respectively. The (204)
XRD reflexion is pointed out (open orange square).
According to the epitaxial relationship (Sect. 4.2.1), (hkl) reflexions of both
BiMnO3 and SrTiO3 are coincident in ϕ angle and, due to the similar lattice of both
compounds, they take place in similar 2θ and ω angle, which means similar qparallel and
qperp in the RSM. Thus, as in ϕ scans, the criterion of choosing the appropriate
asymmetric reflexion is based on looking for a sufficiently intense XRD peak of the
123
Chapter 4. BiMnO3 thin films
film, but also with large enough angular separation with regard to the substrate reflexion
in order to be able to discern between both contributions (film + substrate) in the
reciprocal space map. Taking into account the geometric configuration of the 4-circle
diffractometer (Fig. 2.4), and using [100] and [001] vectors as the in-plane and out-ofplane directions (note that for BiMnO3 the out-of-plane direction is [010]), respectively,
Fig. 4.11 depicts the allowed XRD reflexions in the reciprocal space, considering
BiMnO3 film relaxed, i.e. with bulk pseudocubic lattice parameter (~3.95 Å). It is worth
recalling that both [100] and [001] directions are equivalent when it comes to
characterising the in-plane lattice parameters since BiMnO3 possesses a tetragonal
structure according to the epitaxial relationship (see sect. 4.2.1). Thus, both (hk0) and
(0kl) XRD reflexions of BiMnO3, accomplishing h = l, are equivalent.
XRD reflexion
2θ(º)
ω(º)
ψ(º)
(204) SrTiO3
123.8
35.3
0
(240) BiMnO3
120.0
33.7
0
Table 4.4 – Four-circle diffractometer angles at which the (204) reflexion of SrTiO3
and (240) reflexion of BiMnO3 takes place, when ψ is forced to be 0. ϕ angle is four
times degenerated and placed at 0º, 90º, 180º and 270º.
As shown in Fig. 4.11, q position of (h0l) and (hk0) XRD reflexions of substrate
and film, respectively, are very similar. (204) and (240) XRD reflexion (substrate and
film, respectively) was used (open orange square), which corresponds to a high-2θ
reflexion, and hence the angular separation is large, but with enough intensity to be
recorded. In RSM, instead of fulfilling the condition of ω = θ, as in the ϕ-scans, ω is
modified as follows ω = θ – ψ (see table 4.4), forcing ψ = 0, allowing the asymmetric
(204) and (240) reflexion to diffract. Note that ψ angle corresponds to the angle between
the out-of-plane direction and the perpendicular direction of the (204) crystallographic
planes [(240) in the case of BiMnO3], as shown in Fig. 2.4.
124
Chapter 4. BiMnO3 thin films
Fig. 4.12 – Reciprocal space
map
around
(204)
XRD
reflexion of SrTiO3 and (240)
XRD reflexion of BiMnO3 phase
of 50-nm thick films grown at
0.1 mbar of O2 pressure and (a)
630ºC, (b) 645ºC and (c) 660ºC
125
Chapter 4. BiMnO3 thin films
In the RSM q is not directly measured, but, instead, several coupled 2θ/ω XRD
scans are performed for different ω values, giving rise to a 2D 2θ – ω map of intensities.
Then, using Eq. (2.8), qperp and qparallel are obtained (see Sect. 2.1). As an illustrative
example, Fig. 4.12 (a) shows the RSM of (204) and (240) XRD reflexions of SrTiO3
substrate and 50-nm BiMnO3 film (grown in the optimised deposition conditions for
single-phase stabilisation, i.e. 630ºC and 0.1 mbar of O2 pressure), respectively. As qperp
= k/b = 4/b [see Eq. (2.6)], where b is the out-of-plane lattice parameter of BiMnO3,
BiMnO3 peak is found at lower values of qperp than that of the substrate since SrTiO3
out-of-plane lattice parameter is smaller. Instead, qparallel of BiMnO3 XRD reflexion is
found to be coincident with that of the substrate (indicated by the two guide-to-eye
dashed lines corresponding to Kα1 and Kα2). As qparallel = h/a = 2/a [see Eq. (2.6)], where
a is the in-plane lattice parameter, it means that BiMnO3 in-plane lattice parameter
adopts the value of the SrTiO3 lattice parameter (3.905 Å). As the film in-plane lattice
parameter (3.905 Å) is smaller than that of the bulk (triclinic representation, 3.935 Å),
BiMnO3 films are compressive strained, about -0.76%, defined as following:
strain =
a film − abulk
abulk
= −0.76%
(4.1)
where afilm and abulk are the in-plane lattice parameter for the film and for the bulk lattice
parameter (triclinic representation) of BiMnO3, respectively.
Exploring RSM for Bi – Mn – O films prepared at higher temperatures [Fig. 4.12
(b) and (c)], BiMnO3 phase coherently grows on SrTiO3, i.e. with the same in-plane
lattice parameter, despite its coexistence with parasitic phases of Bi – Mn – O system
(See Sect. 4.1.1). Nonetheless, qperp component of q( 240) of BiMnO3 is increasing on
increasing temperature, which indicates that the out-of-plane lattice parameter of
BiMnO3 phase decreases upon temperature, as found in the symmetric θ/2θ XRD scans
(sect. 4.2.1). Fig. 4.13 (a) shows the in-plane (left axis) and the out-of-plane (right axis)
lattice parameter, computed by means of the RSM, as a function of the deposition
temperature. Note that the BiMnO3 lattice parameters obtained by RSM are computed
from Δqparallel and Δqperp between q( 240) of BiMnO3 and q( 204) of SrTiO3, using that of
SrTiO3 as a reference, with lattice parameter (3.905 Å), accounting for the experimental
126
Chapter 4. BiMnO3 thin films
error (see Appendix C). As observed, whereas in-plane lattice constant is roughly
constant around 3.905 Å (the SrTiO3 lattice parameter), the out-of-plane lattice
parameter is reduced at high deposition temperatures, which bears out the reduction of
the BiMnO3 unit cell volume at high temperatures [Fig. 4.13 (b)]. Nevertheless, the film
unit cell is smaller than that of the bulk (marked with black dashed line in Fig. 4.14) in
all temperature range, ranging from -1.2% to -1.8% in the samples prepared at the
highest temperature. This unit cell volume reduction might be caused by the presence of
Bi vacancies, even for samples prepared at low temperatures, as inferred by the
chemical analysis (Fig. 4.3).
Fig.
4.13
–
(a)
Lattice
parameters of BiMnO3 phase
of Bi – Mn – O thin films as a
function of the deposition
temperature. (b) Unit cell
volume of BiMnO3 phase as a
function of the deposition
temperature. Black dashed
line indicates the bulk unit
cell volume.
Exploring RSM for different thick films no relaxation is observed, i.e. qparallel of
(240) BiMnO3 reflexion and (204) SrTiO3 reflexion are still coincident up to at least 70
nm (thicker films, with strong multiphase character, were not assessed). This is likely
due to the small mismatch between lattice parameters of BiMnO3 and SrTiO3.
127
Chapter 4. BiMnO3 thin films
4.2.3 Surface topography
Fig. 4.14 – Evolution of the surface topography (Field emission SEM images) as a
function of the deposition temperature: (a) 600ºC, (b) 615ºC, (c) 630ºC, (d) 645ºC and
(e) 660ºC.
Most of the applications in which a multilayer structure of nanometric films is
required (tunnel junctions, spin valves, etc) the surface morphology plays an essential
role. In addition, studying the surface topography contributes to the understanding of
the growth mechanism of BiMnO3 thin films on SrTiO3, which may be extended to
other similar substrates in perovskite structure with similar lattice parameters. Field
128
Chapter 4. BiMnO3 thin films
emission ESEM and AFM was used in the characterisation of surface topography, as
explained in Sect. 2.3.1 and 2.3.2, respectively.
The effect of the deposition temperature on the surface morphology of the films is
summarised in figure 4.14, in which, illustratively, is depicted 5 films of around 50 nm
of thickness deposited at 600ºC, 615ºC, 630ºC, 645ºC and 660ºC, respectively. All the
images suggest BiMnO3 being formed from three dimensional (3D) growth mechanism
as an evident island morphology is observed. Yet an evolution of the grains with the
temperature can be also noticed. The size of the grains is enlarged on being increased
the temperature. In addition, it can be also observed that the grains are increasingly
defined and more faceted as the deposition temperature rises. These results are
consistent with the thermodynamic aspects of nucleation as the critical nucleus size,
from which the nucleation takes place, is enlarged when the temperature is increased
[16]. It can also be understood as a better arrangement of the arriving species when the
temperature increases since their mobility on the surface increases as well.
Nevertheless, just as at lower temperatures than around slightly above 630ºC only
one modal of distribution of grains is observed, at higher temperatures the films present
a bimodal distribution of grains as well as regions on which there is not a clear defined
morphology. Most of the crystallites on the films deposited at higher temperatures have
a flat surface, corresponding to the same crystallites formed at lower temperatures, but
there is a minor second family of grains which has a pyramidal-like shape. This second
family of crystallites might be related to the presence of Mn-rich parasitic phases as at
higher temperatures XRD scans has revealed the formation of Mn3O4 and Bi2Mn4O10,
apart from BiMnO3. What is more, this minor second family has a greater presence at
660ºC than at 645ºC, which would be in agreement with the increasing intensity of
diffracted peaks of the Mn-rich phases upon temperature (Fig. 4.1). The presence of
different family of crystallites for BiMnO3 and Mn3O4 in the ternary Bi – Mn – O films
is also reported by Fujino et al. [2]. Interestingly enough is the fact that the presence of
regions with no clear morphology increases upon temperature, which might be related
to amorphous/polycrystalline Mn-rich regions due to the small [Bi]/[Mn] cationic ratio
of the films prepared at the highest temperatures (Fig. 4.3). However, the multiphase
character of Bi – Mn – O films at low temperatures shown in the XRD scans cannot be
observed from the surface morphology images.
129
Chapter 4. BiMnO3 thin films
Fig. 4.15 – Illustrative AFM topographic image of 60-nm thick BiMnO3 thin film grown
at 630ºC and 0.1 mbar of O2 on (001)-oriented SrTiO3 substrate.
AFM topographic images bear out the clear island surface morphology of BiMnO3
thin films grown on SrTiO3 (Fig. 4.15), indicative of a 3D growth mode. Consequently,
notably rough surfaces are found, with typically root-mean-square (rsm) surface
roughness of 5 nm (3 nm in the best-case scenario).
4.3 Magnetic properties of Bi –
Mn – O films
As explained in chapter 1, the ferromagnetic order in BiMnO3 results from a
peculiar eg orbital ordering of Mn3+ cations, which makes ferromagnetic interactions
dominate over the antiferromagnetic ones [5]. Nonetheless, this delicate balance
between antiferromagnetic and ferromagnetic may substantially be modified as a
consequence of the epitaxial strain [17]. Moreover, Bi-deficient samples [3] and
multiphase character of Bi – Mn – O system [2] makes the magnetic characterisation
even more complicated. Here we study the magnetic properties of both single-phase
BiMnO3 films and multiphase Bi – Mn – O films, carried out by the SQUID
magnetometer (Sect. 2.5.1). The applied magnetic field, H, has been applied along an
130
Chapter 4. BiMnO3 thin films
in-plane direction. The large diamagnetic contribution of the substrate SrTiO3 was
removed from the raw data (see Appendix D).
The temperature dependence of the magnetisation, M(T), of single-phase 50-nm
BiMnO3 is illustrated in Fig. 4.16 (c), whose XRD pattern is shown in Fig. 4.16 (a). The
sample was cooled down under an applied in-plane magnetic field, H, of 1000 Oe. The
ferromagnetic transition temperature occurs at TFM ~ 100 K, in close agreement with the
reported bulk value ~105 K [7], as inferred by the differentiated inverse of the volume
magnetic susceptibility 1/χv (Fig. 4.16 (c); right axis). Note that χv is computed by M/H
once the diamagnetic contribution of SrTiO3 substrate is removed. Quite different
magnetic behavior is found for thicker films, Fig. 4.16 (d), in which strong multiphase
character is found, Fig. 4.16 (b). The differentiated 1/χv (Fig. 4.16 (d); right axis) shows
two maxima, indicating two ferromagnetic transition temperatures, i.e. at ~50 K and
~100 K of Bi – Mn – O system. Whereas the higher transition temperature must be
related to the BiMnO3 phase, that at 45-50 K must correspond to the Mn3O4 phase
[clearly present in the XRD pattern, Fig. 4.16 (b)], as this compound, with spinel
structure AB2O4: Mn2+ (at the A-site) and Mn3+ (at the B-site), orders
antiferromagnetically below ~45 K [18 – 20], giving rise to net magnetic moment (i.e.
ferrimagnetism, no compensated spins of Mn2+ and Mn3+).
131
Chapter 4. BiMnO3 thin films
Fig. 4.16 – Magnetic properties of Bi – Mn – O films grown at 630ºC and 0.1 mbar of
O2 pressure of 50 nm (a, c, e) and 100 nm (b, d, f) of thickness. θ/2θ XRD scan of
single-phase BiMnO3 film (a) and multiphase Bi – Mn – O film (b). Temperature
dependence of the magnetization (left axis) and derivative of the inverse susceptibility
(right axis) of BiMnO3 thin film (c) [the corresponding XRD pattern in (a)] and Bi – Mn
– O film (d) [the corresponding XRD pattern in (b)] under an in-plane applied
magnetic field of 1000 Oe. (e) Magnetic field dependence of the magnetization of
BiMnO3 thin film [the corresponding XRD pattern in (a)] at 10 K. Bottom panel: Zoom
of the low field region. (f) Magnetic field dependence of the magnetization of Bi – Mn –
O film [the corresponding XRD pattern in (b)] at 10 K.
132
Chapter 4. BiMnO3 thin films
Fig. 4.16 (e) shows magnetisation data versus applied magnetic field, M(H),
recorded at 10 K, for single-phase BiMnO3 films [XRD pattern Fig. 4.16(a)], in which
an hysteretic M(H) behaviour can clearly be observed, confirming the ferromagnetic
character of BiMnO3 thin films, with a coercive field, Hc, found to be around 425 Oe.
Yet the multiphase Bi – Mn – O film [XRD pattern Fig. 4.16 (b)] shows a quite broader
M(H) curve [Fig. 4.16 (f)], reflecting the contribution of the ferrimagnetic Mn3O4 phase,
which displays larger coercive fields [18 – 20], and the likely magnetic coupling with
the ferromagnetic BiMnO3 phase. Moreover, M(H) curve of Bi – Mn – O films [Fig.
4.16 (f)] shows lower saturated magnetisation (~120 emu/cm3) than that of pure
BiMnO3 phase (~375 emu/cm3) [Fig. 4.16 (e)], which is due to the reduced magnetic
moment of Mn3O4 phase (1.5 – 1.8 μB/f.u.) [18 – 20] compared to that of BiMnO3 (~3.6
μB/f.u. in bulk [7]).
It is worth noting, though, that the saturated magnetisation for single-phase BiMnO3
films [Fig. 4.16 (e)] is found to be much lower (375 emu/cm3 corresponds to ~2.5
μB/f.u.) than that of bulk specimens. Similar low magnetisation values were reported for
BiMnO3 thin films (1.5 – 2.5 μB/f.u. [2, 3, 17, 21 – 23]). The smaller saturation moment
in thin film was argued to be driven by the enhancement of the inherent magnetic
frustration in BiMnO3 [17]. It is to be noted that in bulk BiMnO3 two out of three
magnetic interactions are ferromagnetic, dominating over the antiferromagnetic ones
[5]. Yet the strength of the ferromagnetic and antiferromagnetic interactions can be
modified by the epitaxial strain as it changes the inter-ion distances and angles,
unbalancing the bulk equilibrium between the two kinds of magnetic interactions [17].
However, on the other hand, off-stoichiometric films, in particular Bi-deficient samples
may also produce a strong reduction of the magnetisation of BiMnO3 films [3]. By
electric equilibrium of the compound each Bi vacancy originates three Mn4+
neighbouring ions, which are not subjected to Jahn-Teller distortion like Mn3+ and
consequently contribute to the local disruption of the peculiar orbital ordering of Mn3+
ions responsible for the ferromagnetic ground state of BiMnO3. Moreover, each Mn4+
(t2g3eg0) may couples either antiferromagnetic or ferromagnetic with the surrounding
Mn3+ (t2g3eg1) depending on the local configuration, i.e. weather empty eg orbital points
toward empty eg orbital or half-filled eg orbital, respectively (Sect. 1.2.3). The local
competing ferromagnetic/antiferromagnetic interactions lead to a strong spin frustration.
Indeed, not only Mn4+ couples antiferromagnetically with the Mn3+ matrix, but also
133
Chapter 4. BiMnO3 thin films
several first neighbour Mn3+ ions in the vicinity of a Bi vacancy [3]. Taking into
account the high Bi volaitility and that just 0.05% of Mn4+ concentration can produce a
~40% reduction of the magnetisation [3], this latter scenario seems to be the most
plausible when it comes to describe the magnetic properties of our BiMnO3 films. Note
that this small amount of Mn4+ is hardly detectable by chemical analysis techniques.
However, both chemical composition (Sect. 4.1.1) and structure characterisation (Sect.
4.2) suggest some Bi-deficiency in BiMnO3 films, which would be in agreement with
the small recorded magnetisation. Indeed, the fact that all reported magnetisation data of
BiMnO3 films [2, 3, 17, 21 – 23] display reduced magnetic moments evidences the
difficulty in obtaining high-quality stoichiometric BiMnO3 thin films.
4.4 Electric and magnetoelectric
properties
4.4.1 Background
One of the interesting features multiferroic materials may exhibit is the so-called
magnetoelectric coupling (as explained in Sect. 1.1.3), which consists of the coupling
between the ferroelectric and the magnetic order. A common route to investigate the
magnetoelectric character consists of studying the effect on the dielectric permittivity, ε,
of changes of the magnetic state of the magnetic layer, either by applying a magnetic
field, the so-called magnetocapacitance (or magnetodielectric response), ε(H), or by
searching for variations of ε in the temperature dependence, ε(T), in the vicinity of the
magnetic transition temperature (see Sect. 1.1.3).
BiMnO3 bulk polycrystalline samples were reported to display a modest dielectric
permittivity (εr ~ 25) at low temperatures (50 K – 170 K) [7]. The reported dielectric
constant shows an steady increasing value upon temperature. Interesting enough, the
dielectric permittivity of BiMnO3 bulk polycrystalline samples displayed a slight
anomaly (a subtle peak increase) around the ferromagnetic transition temperature (TFM
~ 100 K) [7]. Moreover, the dielectric response showed a weak magnetic field
dependence, in which the magnetodielectric effect, MC = [ε(H)-ε(0)]/ε(0), scales with
134
Chapter 4. BiMnO3 thin films
the square of the magnetisation, M2, being maximum (0.6%) at T ~ TFM [7]. Both
features suggested that the two ferroic orders of BiMnO3 are coupled. On the other
hand, the dielectric behaviour of BiMnO3 thin films were analysed by impedance
spectroscopy [24, 25], in which, despite discrepancies on the value of the dielectric
permittivity with regard to that of bulk samples, similar anomalies were found around
TFM. Yet the magnetic dependency of the dielectric properties of BiMnO3 thin films
remains to be elucidated.
Here in this section we performed an exhaustive study of the dielectric properties of
BiMnO3 thin films, in which temperature dependent impedance spectroscopy (see Sect.
3.2) was used to disentangle extrinsic and intrinsic contributions to the measured
permittivity. At the end of the section, the intrinsic magnetoelectric response of BiMnO3
thin films is obtained by deconvoluting magentodielectric and magnetoresistive effect
(see Sect. 3.2.4). To performed the dielectric measurements, Pt/BiMnO3/Nb:SrTiO3
capacitors were fabricated (see Sect. 3.1). BiMnO3 samples were grown at the optimised
conditions for single-phase formation (i.e. at 630 ºC and 0.1 mbar of O2 pressure). The
thickness of the set of samples was comprised between 40 and 60 nm.
4.4.2 Complex dielectric constant and ac
conductivity. Qualitative analysis
Fig. 4.17 shows the temperature, T, evolution of the dielectric permittivity at
different frequencies, assuming that the measured capacitance is only due to the
dielectric response of BiMnO3 film, i.e. C = ε’ε0A/(2t) (see chapter 3). As observed,
ε’(T) displays a clear step-like increase on increasing temperature. Moreover, this steplike feature moves toward higher temperatures on increasing the measuring frequency.
As a result, ε’(T) shows two plateaus: at high and low temperatures. Whereas the value
of the dielectric permittivity at low temperatures is almost frequency independent and
close to the bulk values (~ 25), that of the high temperatures is anomalous high and
highly frequency dependent. As described in sect. 3.2, these features are clearily
indicating that extrinsic contributions are likely altering the dielectric response of
BiMnO3 films.
135
Chapter 4. BiMnO3 thin films
Fig. 4.17 – Temperature dependence of the dielectric response of Pt/BiMnO3/Nb:SrTiO3
system measured at different frequencies.
In order to assess the frequency response, the complex representation of the
dielectric constant, ε* = ε’ – iε”, will be used (see Sect. 3.2.2). Fig. 4.18 depicts the
frequency dependence, ν, of the real part (top panel), ε’, and the imaginary part (bottom
panel),
ε”,
of
the
complex
dielectric
constant.
The
measured
ε’
of
Pt/BiMnO3/Nb:SrTiO3 capacitors shows two frequency regimes, where ε’(ν) is rather
constant, separated by a step-like region which is accompanied by a peak in ε”(ν). Both
the sharp increase in ε’(ν) and the peak in ε”(ν) shift toward higher frequencies on
increasing temperature. At first sight, this behaviour shows a clear resemblance of a
thermally activated Debye-like dielectric relaxation dominating the frequency
dependence of ε’(ν) [26]. Yet, as described in Sect. 3.2.3, a Maxwell-Wagner relaxation
type, in which two electric contributions (characterised by two RC-elements) to the
dielectric properties of the system is found, may reproduce identical dielectric
behaviour, following the same temperature evolution depicted in Fig. 4.18 if the
resistance of either of each RC-element decreases upon temperature. Indeed, the
measured value of ε’ in the low frequency plateau is anomalous large (~ 450 – 500),
whereas that obtained from the high frequency plateau (~ 35 – 40) is in a similar range
of the dielectric permittivity found in BiMnO3 bulk samples [7], thus indicating a more
plausible intrinsic character.
136
Chapter 4. BiMnO3 thin films
Fig. 4.18 – Frequency dependence of the real part (top panel) and the imaginary part
(bottom panel) of the complex dielectric constant of Pt/BiMnO3/Nb:SrTiO3 capacitors
measured at different temperatures.
For an ideal dielectric behaviour ε’ should be frequency independent (see Fig. 3.7 in
Sect. 3.2.2). Yet it is worth noting that ε’(ν) modestly decreases on increasing frequency
in the high-frequency plateau, following the same trend described for non-ideal
dielectrics (see Fig. 3.8 in Sect. 3.2.2). This non-ideality can better be appreciated in the
complex conductivity, σ* = i·ωε0ε*, in which the real part, σ’, of σ* at various illustrative
temperatures is plotted in Fig. 4.19. In the log-log scale of σ’(ν), Fig. 4.19, at highfrequencies there is a power-like frequency dependence, ~ να, which is in agreement
with the Jonscher’s universal dielectric response of non ideal dielectrics [26 – 28]. This
frequency dependent term is superimposed to a non-frequency dependent term, the
137
Chapter 4. BiMnO3 thin films
corresponding leakage of the sample: σdc, responsible for the flattening of σ’(ν) at
intermediate frequencies. Thus it reasonably follows σ’ = σdc + σ0·ωα, where ω stands for
the angular frequency (2πν), marked with dashed line in Fig. 4.19, as described in Sect.
3.2.2 for non-ideal dielectrics. However, when further lowering ν, conductivity is
steeply reduced, deviating for the ideal behaviour marked in dashed lines. As shown by
data in Fig. 4.19, this drop is also temperature dependent, and shifts toward higher
frequencies as temperature rises. Not surprisingly, it coincides with the large
enhancement of the dielectric constant and the peak of ε” shown in Fig. 4.18.
Fig. 4.19 – Frequency dependence of σ’ at different temperatures. The dashed line
indicates the non-ideal dielectric behaviour, σ’ = σ’dc + σ’0ωα (see text).
In the following it will be shown that both, the low-frequency region as well as the
step-like region are not-intrinsic properties of BiMnO3 film but result from the
contribution of interface effects.
4.4.3 Impedance spectroscopy. Quantitative
analysis
To obtain a more quantitative insight into the dielectric response of the sample, to
investigate the number of electrical responses present and to determine the intrinsic
138
Chapter 4. BiMnO3 thin films
properties of the film, complex impedance (Z* = Z’ + iZ”) spectroscopy was performed
as described in Sect. 3.2.1.
Fig. 4.20 – (a) Impedance complex plane (–Z’’ – Z’ plots) from impedance data
measured at 150 K. The visual guide of the dashed line indicates the two semicircles at
high and low frequency. The inset sketch depicts the equivalent circuit, describing the
different electrical responses present in Pt/BiMnO3/Nb:SrTiO3 capacitors (see text for
symbols). (b) –Z’’ – Z’ data plots measured at different temperatures.
In Fig. 4.20 (a) illustrative –Z” - Z’ plot of the impedance measured at 150 K is
shown. Data signals the existence of two incomplete semicircles (marked with dashed
lines as guide-to-eyes) at high and low frequency, respectively. The existence of these
two semicircles can be explained by the presence of two electrical contributions to the
dielectric data in Pt/BiMnO3/Nb:SrTiO3 capacitors. Thus, as suspected, the dielectric
response observed in Sect. 4.4.2 does not only come from the intrinsic dielectric
properties of BiMnO3 film, which would produce a unique semicircle (Sect. 3.2.1). This
behaviour is hence consistent with a Maxwell-Wagner relaxation, as explained in Sect.
3.2.3, in which extrinsic dielectric contribution is affecting the measurement.
Nonetheless, it is worth mentioning here that for temperatures lower than ~90 K, only
the high frequency contribution is observed as the low frequency contribution is out of
the frequency range, i.e. it appears at frequencies lower than 20 Hz. Instead, for
temperatures higher than 200 K, only the low frequency contribution is found in the
139
Chapter 4. BiMnO3 thin films
frequency spectra as the high frequency contribution appears at frequencies higher than
1 MHz, i.e. not experimentally available.
On the other hand, it can be appreciated in Fig. 4.20 (a) that the radius of the lowfrequency semicircle is much larger than the high-frequency one; this reflects that the
low-frequency contribution is much more resistive than that of the high-frequency
contribution. Additionally, inspection of the impedance data at different temperatures,
shown in Fig. 4.20 (b), indicates that the high frequency semicircle significantly
decreases on increasing temperature, evidencing that the resistivity of the high
frequency contribution decreases as temperature rises, according to data of the
conductivity shown in Fig. 4.19.
Thus, according to Fig. 4.20, the most natural explanation of the dielectric
behaviour shown in section 4.4.2 comes from the formation of a capacitive layer at the
interface and by the temperature dependence of the resistivity of the core of the film, as
deduced in Sect. 3.2.3. The band bending caused by the difference between the work
function of the metal and the electronic affinity of the dielectric gives rise to charge
depletion/accumulation region at the interface [24, 27, 29, 30], which forms a relatively
thin layer, behaving as a high resistive barrier, modelled as a capacitor, Cext, and a low
conductance, Rext-1, connected in parallel as illustrated by the circuit-model sketched in
Fig. 4.40 (a). At high frequency, charge carriers have no time to follow the alternating
electric field and the measured capacitance is the film and the interface capacitances in
series (Fig. 4.21). However, at low frequencies, charge carriers do respond to the
electric field in the low resistive part, i.e. the core of the film [modelled as R inset Fig.
5.42 (a)], forming an electric current. This entails that the drop of the electric field is
mostly taking place at the interface barrier, yielding the apparent high dielectric
constant shown in Fig. 4.18 because of the apparent reduction of the dielectric thickness
(measured capacitance ~ 1/t’) as shown in Fig. 4.21 [29]. On increasing temperature, the
film resistivity decreases [so leakage, σdc, increases (Fig. 4.19)] and charge carriers can
respond to faster alternation of the electric field. Thus, the apparent enhancement of the
dielectric constant due to the apparent reduction of the dielectric thickness is shifting
toward higher frequencies on increasing temperature, consistent with the observed
temperature evolution of data of Fig. 4.18. The cut-off frequency, ωmax, at which losses
140
Chapter 4. BiMnO3 thin films
(∼ε’’) show a peak [Fig. 4.18] is given by the condition ωmax(T) = [R(T)·C]-1 [29] and is
therefore temperature dependent. Hence, the thermal activation of this apparent
dielectric relaxation is driven by the temperature-dependence of the resistivity, instead
of permanent dielectric dipoles. Indeed, the dielectric relaxation of permanent dipole
moments tends to occur at much higher frequencies, in the range of the microwaves
[31], as indicated in Sect. 3.2.2.
Fig. 4.21 – Sketch of the dielectric behaviour of BiMnO3 thin films when the resistivity
of the film and interface parasitic capacitance interfer.
141
Chapter 4. BiMnO3 thin films
Fig. 4.22 – Experimental data (black solid symbols) and fitting (red solid line) using the
model of Eq. 4.2 for some illustrative temperatures.
The impedance of Pt/BiMnO3/Nb:SrTiO3 system, in which the intrinsic film and the
interface contributions are accounted, is given by adapting of Eq. 3.10 in Sect. 3.2.3:
Z * ( R − CPE , Rext − Cext ) =
Rext
R
+
α
1 + iω ⋅ Rext ⋅ C ext
1 + R ⋅ Q ⋅ (iω )
(4.2)
where the first and the second terms correspond to the film and the extrinsic
contributions, respectively. A CPE element (see Sect. 3.2.1) is used for the film
contribution accounting for the non-ideality of the dielectric behaviour of BiMnO3 film
shown in the previous section. Yet for temperatures lower than 110 K, only the intrinsic
142
Chapter 4. BiMnO3 thin films
R–CPE circuit was used as only one electric contribution to the impedance data was
found in the frequency range:
Z * ( R − CPE ) =
R
1 + R ⋅ Q ⋅ (iω )α
(4.3)
Eq. 4.2 and 4.3 was used to fit impedance data in order to validate the proposed
model. Fig. 4.22 shows some illustrative results of the fits to -Z’’– Z’ data at different
temperatures. As observed, model (solid lines) and data match very reasonably, which is
also extensive for the rest of temperatures up to 160 K. Above this temperature the lowfrequency contribution dominates almost completely the experimentally available
frequency range (up to 1 MHz), and reliable determining the intrinsic properties (highfrequency contribution) was unfeasible. The fitting values of the R–CPE (Q, R, α)
corresponding to the film contribution are summarised in table 4.5.
Temperature
(K)
20
30
40
50
60
70
79
84
89
94
99
104
109
114
118
126
138
148
158
Q [Fsα-1]
2.44·109
2.52·109
2.61·109
2.70·109
2.82·109
2.97·109
3.22·109
3.45·109
3.76·109
4.21·109
5.04·109
6.41·109
7.23·109
8.11·109
9.21·109
1.22·108
1.76·108
2.98·108
7.61·108
error Q
[%]
0.3
0.4
0.4
0.5
0.6
1.1
1.5
1.8
2.3
3.1
4.7
7.6
6.5
7.9
9.3
9.8
10.1
12.0
13.1
R [Ω]
9.29·107
7.82·107
7.38·107
6.84·107
6.12·107
3.09·107
1.86·107
1.14·107
6.59·106
3.57·106
1.89·106
9.36·105
1.74·105
8.94·104
4.42·104
1.15·104
3.50·103
1.29·103
5.43·102
error R
[%]
13.3
13.2
14.3
15.1
16.0
19.5
16.0
12.6
9.8
7.8
7.4
7.7
4.6
4.4
4.6
4.3
4.4
4.2
4.6
α
0.986
0.984
0.982
0.980
0.978
0.975
0.970
0.965
0.959
0.951
0.939
0.921
0.927
0.918
0.909
0.894
0.874
0.844
0.789
error α
[%]
0.03
0.04
0.04
0.05
0.05
0.11
0.15
0.18
0.23
0.31
0.47
0.76
0.61
0.73
0.90
1.10
1.35
1.52
1.98
Table 4.5 – Fitting results of the high-frequency R-CPE element, sketched in Fig. 4.20
(a).
143
Chapter 4. BiMnO3 thin films
It is worth noting that the CPE exponent, α, decreases upon temperature (Fig. 4.23),
signalling an increasing non-ideality of the dielectric behaviour of BiMnO3 film on
increasing temperature. Remarkably enough, α shows an anomaly around 100 K,
possibly reflecting the set of the magnetic order.
Fig. 4.23 – Temperature dependence of the CPE exponent.
From the fitting values (Q, R, α), the intrinsic dielectric permittivity [ε = C·(2t/ε0A),
where C = (Q·R)(1/α)/R, see Appendix C] and the intrinsic resistivity [ρ = A·R/(2t)] of
BiMnO3 film can be computed at each temperature, as shown in Fig. 4.24 and 4.25,
respectively. For the sake of clarity in the text, in the following dielectric permittivity
and resistivity stand for the intrinsic ones of BiMnO3 films, computed by impedance
spectroscopy as stated above.
The temperature dependence of dielectric permittivity, ε(T), of BiMnO3 films (Fig.
4.24, top panel) shows a modest steady increase up to ~70 K, consistent with the slight
increase found in the dielectric permittivity of bulk specimens in similar range of
temperatures [7]. However, above ~80 K, ε(T) upturns, displaying a peak structure
around 105 K, close to the ferromagnetic temperature. This anomaly can be better
appreciated in the derivative of the dielectric permittivity with respect to temperature
(Fig. 4.24, bottom panel), in which clearly there is a pronounced change around the
magnetic transition temperature (marked with dashed line). This peak in ε(T) is in close
agreement with previous work, both in thin films [25] and bulk [7], and it may well
144
Chapter 4. BiMnO3 thin films
represent the intrinsic magnetoelectric coupling of BiMnO3 compound. Note that
extrinsic contributions cannot be the origin of this anomaly as they have been
previously disentangled from the raw impedance data.
Fig. 4.24 – Temperature dependence of the dielectric permittivity (top panel) and its
derivative (bottom panel) of BiMnO3 thin films. The dashed line indicates the
ferromagnetic transition temperature.
The temperature dependence of the resistivity, ρ(T), of BiMnO3 thin films (Fig.
4.25) shows a semiconductor-like behaviour, similar to what has been reported in
previous work and related perovskite oxides [7, 8, 22, 24, 32]. The resistivity values are
145
Chapter 4. BiMnO3 thin films
found to decrease upon temperature, from ~1010 Ω·cm at 20 K to ~105 Ω·cm at 160 K.
Yet data shows two different regimes for low and high temperatures reflecting a change
in the predominant conduction mechanism:
i)
Above ~100 K, the conduction mechanism is thermally activated, for which
ρ(T) follows an Arrhenius law (indicated as dashed line in Fig. 4.25), ρ(T) =
ρ0exp[-Ea/(kBT)], with an activation energy value Ea ~ 184 meV.
ii)
Below ~100 K, instead, ρ(T) monotonously deviates from the Arrhenius law,
in which the thermal activation of charge transport is weakened or becoming
negligible as inferred by the reduced slope of the ρ vs 1/T curve.
Fig. 4.25 – Temperature dependence of the resistivity of BiMnO3 films. The dashed line
shows the Arrhenius fitting (see text). Dashed region indicates the magnetic Curie
temperature.
In order to fit the ρ(T) data in all experimental temperature range, alternative
conduction mechanism, such Mott’s Variable-Range-Hopping (VRH) or Efros and
Shklovskii VRH conduction mechanisms [ρ(T) = ρ0exp(T0/T1/γ), γ = 4 or 2, respectively]
146
Chapter 4. BiMnO3 thin films
have been considered [33 - 37]. Yet it is found that none of these models (Fig. 4.26)
allow describing satisfactorily the whole temperature range, either. Moreover, VRH
model, in which electron hopping is not produced between first neighbour ions but there
is an optimum hopping distance that maximise the hopping probability [37], is proposed
for either disordered systems or with doping impurities, in which localised states are
found. As this case is not expected in BiMnO3 films, the conduction mechanism shown
in Fig. 4.25 has more physical meaning. In any case, data in Fig. 4.25 suggests either a
change of the transport mechanism or the relevant energy for activated transport
occurring at about 100 K. Remarkably enough, this change in the conduction
mechanism appears close to the ferromagnetic transition temperatures, indicating that
the set of the magnetic order may have some influence in the conductivity of BiMnO3
compound.
Fig. 4.26 – Resistivity of BiMnO3 films as a function of (1/Tempereture)1/γ, being γ =2
(a) and γ = 4 (b). The dashed region indicates the ferromagnetic Curie temperature.
Above 100 K, the activation energy (Ea ~0.18 eV) of the semiconducting behaviour
of BiMnO3 films gives an estimation of the energy gap between the conduction and
valence bands. Similar activation energies are found in previous work on BiMnO3 thin
films [22, 24, 25]. Yet it is worth noting that optical measurements reveal a much larger
band gap in BiMnO3 compounds, around 1.1 eV [23].
147
Chapter 4. BiMnO3 thin films
4.4.4 Magnetoelectric response
Data shown in previous section points to the occurrence of magnetoelectric
coupling in BiMnO3 films as inferred from the clear anomaly of ε(T) curve around the
magnetic transition temperature (Fig. 4.24). In order to bear out this plausible
magnetoelectric effect, magnetic field, H, dependent dielectric measurements were
performed. Yet it is also clear form data in previous section the presence of extrinsic
and intrinsic electric contributions in Pt/BiMnO3/Nb:SrTiO3 capacitors. This fact,
together
with the possibility of BiMnO3 displaying
a certain degree of
magnetoresistence, can evoke an apparent magnetic-field dependent dielectric
permittivity without magnetoelectric coupling (see Sect. 3.2.4). In order to avoid any
misleading interpretation and to be able to disentangle between genuine magnetoelectric
coupling –i.e. genuine changes in ε(H)– from pure magnetoresistive effects, impedance
spectroscopy was performed at selected fixed temperatures under different magnetic
fields (see Sect. 3.2.4).
Fig. 4.27 – Impedance complex plane (–Z’’ – Z’ plots) from impedance data measured
at 95 K under different magnetic fields, H.
148
Chapter 4. BiMnO3 thin films
Fig. 4.27 depicts the magnetic field dependence of the impedance data of
Pt/BiMnO3/Nb:SrTiO3 capacitors measured at 95 K. Note that this temperature was
selected for being close to the magnetic Curie temperature, thus expecting large
magnetoelectric effect as indicated in Fig. 4.24. Qualitatively, as observed in Fig. 4.27,
on increasing the applied magnetic field, the semicircle diameter of the –Z’’ – Z’ plots
decreases, signalling that the resistivity of BiMnO3 decreases upon applied magnetic
field. Using the same procedures as described in previous section, i.e. using Eq. 4.3 to
fit the impedance data under the different magnetic fields, the fitting values (Q, R, α) of
the R–CPE element can be determined at each magnetic field. As discussed in previous
section, these values are used to compute the magnetic field dependence of the intrinsic
resistivity, ρ(H), and dielectric permittivity of BiMnO3 films, which are assessed in the
following.
Fig. 4.28 – Magnetic-field dependence of the resistivity of BiMnO3 films at 95 K
The magnetic field dependence of the BiMnO3 resistivity at 95 K is shown in Fig.
4.28. As observed, ρ(H) decreases on increasing H, confirming the behaviour shown in
Fig. 4.27. Thus, BiMnO3 indeed displays a negative magnetoresistance. The influence
of the magnetic field on the resistivity of BiMnO3 was also inferred in Fig. 4.25, in
which a notably change in the conduction mechanism is observed around the magnetic
transition temperature. Once the magnetoresistive effect is disentangled from the
impedance data, we focus on the possible changes of the dielectric permittivity of
149
Chapter 4. BiMnO3 thin films
BiMnO3 on applying a magnetic field. As shown in the upper part of Fig. 4.29, in which
the ε(H) measured at 95 K is plotted, the dielectric permittivity continuously increases
on increasing the magnetic field, thus displaying a positive magnetocapacitance effect.
This contrasts to the negative magnetocapacitance effect reported for bulk BiMnO3 [7].
It is worth noting that no magnetoresistive artefacts, as described in Ch. 3, are the origin
of this magnetocapacitance, as the resistive and dielectric character have been
disentangled from the raw impedance data previously. Moreover, ε(H) curve shows a
modest hysteretic behaviour, i.e. ε(H) does not follow the same path when increasing H
as when decreasing H. Yet it should be mentioned that error bars (around 5 %) may
mask this hysteretic behaviour. In order to crosscheck the hysteresis in ε(H) curves,
impedance data at different magnetic fields was also recorded at 50 K, from which the
intrinsic dielectric permittivity of BiMnO3 film was obtained by fitting data by Eq. 4.3,
as described previously. The results are shown in the lower part of Fig. 4.29, in which
the ε(H) curve clearly follows the same hysteretic trend as that of 95 K, though in a
more modest fashion probably due to the fact that the closer to the magnetic Curie
temperature the stronger the magnetoelectric effect (see Sect. 1.1.3).
4.29 – Magnetic field dependence of the dielectric permittivity of BiMnO3 films. Solid
(open) symbols are obtained on increasing (decreasing) magnetic field.
Thus, despite the fact that error bars of the fitting inhibit from conclusively stating
the magnetoelectric coupling, especially giving reliable quantitative values, all
150
Chapter 4. BiMnO3 thin films
evidences point to this feature being realised in BiMnO3 compounds. In fact, the
hysteretic behaviour of ε(H) can only be understood as an effect of the magnetic state of
BiMnO3 film on the dielectric permittivity. In particular, as shown in Fig. 4.29,
increasing the magnetic ordering of the spins of Mn3+ (i.e. increasing the magnetisation
by applying a magnetic field) in BiMnO3, the dielectric permittivity increases. Due to
the ferromagnetic character of BiMnO3, when the magnetic field is removed, there is
still a remanent magnetisation in the film, which is responsible for the relatively larger
dielectric permittivity with regard to that at the beginning of the H cycle (i.e. when the
film is not magnetised).
4.4 Ferroelectric properties
By electric characterisation the ferroelectric character of BiMnO3 was not possible
to be confirmed in this work. Conduction current was too large with regard to the
ferroelectric domain switching current that masked any footprint of ferroelectricity. It is
worth mentioning that the recorded saturated polarisation of BiMnO3, though from a not
conclusively ferroelectric hysteresis loop, was of the order of a few nC/cm2 [6], i.e. a
very low value. Thus, this points to a small ferroelectric domain switching current, if
any, which becomes negligible in comparison to the leakage current. Moreover, the
latter is even more significant taking into account that thick (thicker than 80 nm) singlephase BiMnO3 films were not feasible to be grown due to the large Bi-deficiency (see
Sect. 4.1).
151
Chapter 4. BiMnO3 thin films
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Chapter 4. BiMnO3 thin films
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153
Chapter 4. BiMnO3 thin films
154
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Chapter 5
(Bi0.9La0.1)2NiMnO6 thin
films
155
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
156
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
5.1 Single-phase stabilisation
The stabilisation of single phase Bi-based manganite-family perovskites has been,
in general, difficult to achieve because of their tendency of multiphase formation and
the high volatility of bismuth [1 – 4]. Indeed, in bulk form Bi2NiMnO6 is only achieved
in extreme sintering conditions, i.e. at 6 GPa and 800 ºC of mechanical pressure and
temperature, respectively [5].
Still, as explained in Sect. 1.3.1, metastable compounds can be formed by replacing
the mechanical pressure by the epitaxial stress, i.e. using substrates whose lattice
parameters show a low mismatch with those of the compound that is to be formed.
Thus, as pseudo-cubic lattice parameter of Bi2NiMnO6 is a ~ 3.877 Å, SrTiO3 (001)oriented substrates were used, which presented 0.71 % of tensile stress (See table 4.1).
Substrate
SrTiO3
Structure
and
orientation
Cubic
perovskite
(001)
Latt.
parameter
(Å)
3.905
Mismatch with pseudo-cubic
latt. parameter of Bi2NiMnO6
aBi2 NiMnO6 − aSrTiO3
aSrTiO3
= −0.71%
Table 5.1 – Substrate and mismatch with Bi2NiMnO6.
On the other hand, partial replacement of Bi3+ cations by La3+ cations at the A-site
has been proved to facilitate single-phase stabilisation in bismuth manganite compounds
[3], because of the slightly smaller ionic radius of La3+ with regard to Bi3+ (0.130 nm
and 0.131 nm, respectively [6]). It gives rise to a slightly reduced unit cell volume,
without changing the lattice parameters significantly, but exerting the so-called
chemical pressure (see Sect. 1.2.6) which contributes to prevent Bi3+ cations from
desorption during the growth process. Still, in bulk the solid solution (Bi1-xLax)2NiMnO6
remains non-centrosymmetric for x < 0.2 [7], so that 10% of La-doping was used,
allowing the possibility of ferroelectricity to be established.
(Bi0.9La0.1)2NiMnO6 thin films were grown by PLD (See Sect. 2.1) from
stoichiometric targets, in which the primary oxides are found, not the compound itself.
As SrTiO3 is (001)-oriented, we expect (Bi0.9La0.1)2NiMnO6 thin films to grow with the
157
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
c-axis as the out-of-plane direction, i.e. we expect to find only (00l) reflexions in the
symmetric θ/2θ XRD diffractograms.
In order to optimise the deposition conditions, the substrate temperature, the oxygen
pressure during the growth process and the thickness of the films were assessed.
5.1.1 Dependence on Temperature
By keeping the rest of the PLD deposition conditions fixed (see Sect. 2.1), we grow
different samples at different substrate temperatures, ranging from 590ºC to 700ºC.
In Fig. 5.1, XRD θ/2θ scans of films grown at 0.5 mbar at various illustrative
temperatures are shown. The (00l) reflexions of the (Bi0.9La0.1)2NiMnO6 phase can
clearly be observed for temperatures lower than 660 ºC, which take place at 2θ values
slightly higher than the (00l) reflexions of SrTiO3, as expected since the pseudocubic
lattice parameter of (Bi0.9La0.1)2NiMnO6 is smaller than that of SrTiO3. Note that,
having in mind the Bragg Diffracion law (Eq. 2.1), the interplanar distance of the (00l)
reflexions, d00l = c/l, where c is the out-of-plane lattice parameter, is shorter in the case
of (Bi0.9La0.1)2NiMnO6 compound than in SrTiO3 (see Appendix A). The lattice
parameters will be discussed in sect. 5.2.2.
For films deposited at 660ºC and above, (Bi0.9La0.1)2NiMnO6 reflexions are not
found, which should be due to the fact that they might present such a great deficiency in
Bi content –as this element is very volatile– that makes unfeasible the
(Bi0.9La0.1)2NiMnO6 formation or leads to polycrystalline compound. In addition to the
(Bi0.9La0.1)2NiMnO6 reflections, in the patterns of samples prepared at higher and lower
temperatures than 620ºC the NiO phase, (002) reflection, occurring at about 2θ ~ 43.4º
can clearly be observed. The existence of parasitic lines arising from the transition metal
oxides in the Bi – Mn – Ni – O system in the patterns of samples prepared at higher
temperatures should be expected as a consequence of Bi deficits. Although a
compositional study of the (Bi0.9La0.1)2NiMnO6 films grown at different temperatures
has not been carried out, they are expected to behave similar to BiMnO3 films, in which
the Bi-content decay significantly above 640ºC (see Sect. 4.1.1).
158
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.1 – (a) XRD θ/2θ scans of (Bi0.9La0.1)2NiMnO6 thin films (ranging from 60 to 70
nm) grown at 0.5 mbar of O2 and at different temperatures. * denotes the Kβ of (002)
SrTiO3. (b) Zoom of the (001) reflexion of both SrTiO3 and (Bi0.9La0.1)2NiMnO6.
159
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
The reason of the existence of NiO phase at lower temperatures is more uncertain,
although it may result from the lower mobility of the arriving species onto the substrate
which might lead to phase segregations. It is worth noting here the multiphase tendency
of Bi-based manganite family compounds [1 – 4] and the fact that the target does not
contain the compound itself but the mixture of the primary oxides. Metastable
(Bi0.9La0.1)2NiMnO6 compound requires relatively high temperature, thus the use of low
temperatures may result in an incomplete formation of the compound in the Bi – Mn –
Ni – O system.
The XRD pattern of the film prepared at the intermediate temperature (620ºC)
displays only reflections associated to the (Bi0.9La0.1)2NiMnO6 phase without traces of
spurious phases. Hence, single-phase (Bi0.9La0.1)2NiMnO6 is only obtained when the
film is grown at around 620ºC, slightly lower value than the optimal temperature found
by Sakai et al., 630ºC, for Bi2NiMnO6 thin films grown at similar oxygen pressure (0.53
mbar) [8].
5.1.2 Dependence on O2 pressure
By keeping the rest of the PLD deposition conditions fixed (see Sect. 2.1), we grow
different samples at different O2 pressures, ranging from 0.3 mbar to 0.6 mbar.
In terms of single phase formation of (Bi0.9La0.1)2NiMnO6, the oxygen pressure does
not seem to be such a critical deposition parameter (as the temperature is) in the range
we have worked. As illustrated by data in Fig. 5.2 the XRD θ/2θ diffractograms of films
grown at 620 ºC for different oxygen pressures show no evidence of any parasitic phase
and only the (00l) reflexions of (Bi0.9La0.1)2NiMnO6 phase is obtained. This behaviour
greatly contrasts with the single-phase formation of the parental compound BiMnO3,
which was very sensitive to the O2 pressure (see Sect. 4.1.2). It is worth remarking that
the standard procedure of cooling down the sample after the deposition is finished
consists of introducing O2 pressure immediately, attaining 1·103 mbar of pressure when
the film is at 600ºC and keeping that O2 pressure during the rest of the cooling down
process. Yet we have investigated the effects on the single-phase formation of annealing
the sample at 1·103 mbar of O2 pressure and at 450ºC for 1 hour. At any event, singlephase is achieved (Fig. 5.3).
160
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.2 – (a) XRD θ/2θ scans of (Bi0.9La0.1)2NiMnO6 thin films (ranging from 90 to 120
nm) grown at 620 ºC and at different O2 pressures. (b) Zoom of the (001) reflexion.
161
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.3 – XRD θ/2θ scans of BLNMO thin
films of different thickness grown at 620ºC
and 0.5 mbar of O2 pressure. Whereas
bottom diffractogram shows a non-annealed
sample, upper diffractogram shows an
annealed sample at 450ºC and at 103 mbar
of O2 pressure for 1 hour.
5.1.3 Dependence on thickness
By keeping the rest of the PLD deposition conditions fixed (see Sect. 2.1), and
setting the substrate temperature and the oxygen pressure at 620ºC and 0.5 mbar,
respectively, we grow different samples at different number of laser pulses, i.e. different
thicknesses (ranging from 20 to 140 nm in this work).
In Fig. 5.4, XRD θ/2θ scans of films of various illustrative thicknesses are depicted.
In contrast to the clear thickness dependence of the single-phase stabilisation of
BiMnO3 films (Sect. 4.1.3), single-phase stabilisation in (Bi0.9La0.1)2NiMnO6 is not that
sensitive and it is achieved, at least, up to 140 nm, indicative as a lower bound.
Laue oscillations of the (001) Bragg diffraction peak of 20-nm (Bi0.9La0.1)2NiMnO6
film can be made out [Fig. 5.4 (b)], which points out the existence of crystalline
coherence along the full thickness of the film. They are normally observed for thin films
(few tens of nm) when showing high crystal quality, as it will be borne out in the
following section.
162
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.4 – (a) XRD θ/2θ scans of (Bi0.9La0.1)2NiMnO6 thin films of different thickness
grown at 620ºC and 0.5 mbar of O2 pressure. * denotes the Kβ of (002) SrTiO3. (b)
Zoom of the (001) reflexion.
163
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
5.2 Structural characterisation
and surface topography
5.2.1 Texture of the films
First assessment of the crystal quality was focused on the out-of-plane texture of the
film. As explained in Sec. 2.2.1, a way to quantify it is by means of the FWHM of the
rocking curves (ω scans). In this work we have performed the rocking curves around the
(001) Bragg reflexion. This figure of merit is compared to that of the substrate, as being
the latter a single crystal with presumable high quality and free from form factor effects.
Thus, the FWHM of the substrate Bragg reflexion accounts for the instrumental width.
Fig. 5.5 – Rocking curve of the (001) reflexion of both SrTiO3 substrate and 60-nm
(Bi0.9La0.1)2NiMnO6 film grown at 620ºC and 0.5 mbar of O2 pressure.
Rocking curves of the (001) (Bi0.9La0.1)2NiMnO6 and (001) SrTiO3 Bragg reflexions
are illustrated in Fig. 5.5, of a 60-nm (Bi0.9La0.1)2NiMnO6 film grown in the optimised
deposition conditions for single-phase formation. Comparison of the rocking curves
reveals that the FWMH value of the (Bi0.9La0.1)2NiMnO6 peak (0.071º) is comparable to
that of the substrate (0.067º), which is extensive for the rest of film thicknesses up to
140 nm, attaining FWHM values inferior to 0.09º. Thus, (Bi0.9La0.1)2NiMnO6 films
show a very low out-of-plane dispersion of the unit cells, indicating a high crystalline
quality.
164
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
In-plane texture, i.e. how (Bi0.9La0.1)2NiMnO6 unit cells are in-plane oriented, is
characterise by pole figures and ϕ-scans of an asymmetric reflexion (see Sect. 2.2.1),
which allows planes that are not parallel to the interface to diffract. When it comes to
choosing an appropriate asymmetric reflexion, the criterion is based on using an easy
in-plane axis, such as the [100] or [010] SrTiO3 directions, which are equivalent as
being a cubic structure. However, due to the similarity of the lattice parameters of both
SrTiO3 and (Bi0.9La0.1)2NiMnO6, which means similar 2θ angle of the Bragg reflexions,
a high-2θ reflexion was required in order to minimise the substrate contribution to the
pole figures and ϕ-scans of the film, since discernition in 2θ is larger the higher the
angle is. Thus, (204) reflexion was used, whose difference in 2θ between that of
(Bi0.9La0.1)2NiMnO6 and that of SrTiO3 is about 1.5º (see table 5.2).
(204) reflexion
2θ(º)
ω(º)
ψ(º)
SrTiO3
123.8
61.9
26.6
BLNMO
125.3
62.7
25.9
Table 5.2 – Four-circle diffractometer angles at which the (204) reflexion of both
SrTiO3 and (Bi0.9La0.1)2NiMnO6 (BLNMO) takes place. ϕ angle is four times
degenerated and 90º separated when orthogonal in-plane crystal symmetry.
Fig. 5.6 depicts the XRD ϕ-scans of the assymetric (204) reflexion of both substrate
and film of a 125-nm (Bi0.9La0.1)2NiMnO6 film grown in the optimised deposition
conditions for single-phase formation. As shown, only four 90º-ϕ-spaced peaks of the
film are observed, which not only indicates that there are no contributions of
misoriented
in-plane
family
of
crystallites
of
(Bi0.9La0.1)2NiMnO6,
i.e.
(Bi0.9La0.1)2NiMnO6 films are in-plane textured, but also that the crystal symmetry of
(Bi0.9La0.1)2NiMnO6 films corresponds to that which allows an orthogonal square inplane unit cell base, i.e. tetragonal or cubic. In order to ensure the in-plane texture of the
film, pole figures was performed, in which ψ was scanned from 0 to 30, as illustrated in
Fig. 5.7 for a 60-nm (Bi0.9La0.1)2NiMnO6 film grown in the optimised deposition
conditions for single-phase stabilisation. In agreement with the ϕ-scans, Fig. 5.7
reproduces the four 90º-ϕ-spaced peaks of the film, confirming the tetragonal (cubic)
symmetry.
165
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.6 – XRD ϕ-scans around the (204) reflexion of both (Bi0.9La0.1)2NiMnO6 film and
SrTiO3 substrate, of 125-nm thick, grown at 620ºC and 0.5 mbar of O2.
Moreover, the fact that (Bi0.9La0.1)2NiMnO6 ϕ peaks coincide in ϕ angle value with
those of the substrate [Fig. 5.6 (bottom panel) and Fig. 5.7 (a)] shows that
(Bi0.9La0.1)2NiMnO6 films have grown cube-on-cube, i.e. the tetragonal base is
coincident in orientation with that of the cubic substrate (see Sect. 2.2.1). Or, in other
words, the [100] in-plane crystallographic direction of (Bi0.9La0.1)2NiMnO6 film is
parallel to the [100] direction of SrTiO3, which is normally represented by the epitaxial
relationship [100]BLNMO(001)//[100]SrTiO3(001). The cube-on-cube growth is
confirmed along thickness up to 140 nm.
166
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.7 – XRD pole figure around the (204) reflexion of (a) SrTiO3 (STO) substrate (b)
(Bi0.9La0.1)2NiMnO6 (BLNMO) film, of 60-nm thick, grown at 620ºC and 0.5 mbar of O2.
Both out-of-plane and in-plane texture characterisation suggest BLNMO films have
a high epitaxial quality.
5.2.2 Reciprocal space maps and lattice
parameters
Reciprocal space maps (RSM), where qperp component (related to the out-of-plane
lattice parameter) of the reciprocal space vector q is plotted versus qparallel component
(related to the in-plane lattice parameter), were performed in order to determine the film
lattice parameters (both the out-of-plane and in-plane lattice parameters, as long as an
asymmetric XRD reflexion is assessed) and the epitaxial strain of (Bi0.9La0.1)2NiMnO6
films (see Sect. 2.2.1). In the reciprocal space map, not only the film reflexion is
recorded but also that of the substrate, as the (qparallel, qperp) XRD peak position of the
substrate is used to account for the instrumental error (see Appendix A) in order to
determine the correct lattice parameters of (Bi0.9La0.1)2NiMnO6 films.
According to the epitaxial relationship (Sect. 5.2.1), (hkl) reflexions of both
(Bi0.9La0.1)2NiMnO6 and SrTiO3 are coincident in ϕ angle and, due to the similar lattice
of both compounds, they take place in similar 2θ and ω angle, which means similar
qparallel and qperp in the RSM. Thus, as in the pole figures and ϕ scans, the criterion of
choosing the appropriate asymmetric reflexion is based on looking for a sufficiently
167
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
intense XRD peak of the film, but also with large enough angular separation with regard
to the substrate reflexion in order to discern between both contributions (film +
substrate) in the reciprocal space map. Taking into account the geometric configuration
of the 4-circle diffractometer (Fig. 2.4), and using [100] and [001] vectors as the inplane and out-of-plane directions, respectively, Fig. 5.8 depicts the allowed XRD
reflexions in the reciprocal space, considering (Bi0.9La0.1)2NiMnO6 film relaxed, i.e.
with bulk pseudocubic lattice parameter ~3.877 Å. It is worth recalling that both [100]
and [010] directions are equivalent when it comes to characterising the in-plane lattice
parameters since (Bi0.9La0.1)2NiMnO6 possesses a tetragonal structure according to the
epitaxial relationship. Thus, both (h0l) and (0kl) XRD reflexions, accomplishing h = k,
are equivalent.
Fig. 5.8 – Reciprocal space of the allowed XRD reflexions in the 4-circle diffractometer
for both (Bi0.9La0.1)2NiMnO6 (BLNMO) (solid circles) and SrTiO3 (solid squares), when
[100] and [001] crystallographic directions are the in-plane and out-of-plane
directions, respectively. Top and right axis indicates the corresponding in-plane and
out-of-plane reciprocal lattice units of the XRD reflexions, respectively. The (204) XRD
reflexion is marked by an orange square.
168
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
As shown in Fig. 5.8, q position of (h0l) XRD reflexions of both substrate and film
are very similar, so that (204) XRD reflexion was used (orange square), which
corresponds to a high-2θ reflexion, and hence with a larger angular separation, but with
enough intensity to be recorded. It is to be noted that (204) reflexion is that used in the
in-plane texture characterisation; however, in the RSM, ψ angle remains at zero. Then,
instead of fulfilling the condition of ω = θ, as in the pole figures (or ϕ-scans), ω is
modified as follows ω = θ – ψ (see table 5.3), allowing the asymmetric (204) reflexion
to diffract. Note that ψ angle corresponds to the angle between the out-of-plane
direction and the perpendicular direction of the (204) crystallographic planes (see Fig.
2.4).
(204) reflexion
2θ(º)
ω(º)
ψ(º)
SrTiO3
123.8
35.3
0
BLNMO
125.3
36.8
0
Table 5.3 – Four-circle diffractometer angles at which the (204) reflexion of both
SrTiO3 and (Bi0.9La0.1)2NiMnO6 (BLNMO) takes place, when ψ is forced to be 0. ϕ angle
is four times degenerated and placed at 0º, 90º, 180º and 270º.
In the RSM q is not directly measured, but, instead, several coupled 2θ/ω XRD
scans are performed for different ω values, giving rise to a 2D 2θ – ω map of intensities.
Then, using Eq. 2.8, qperp and qparallel are obtained (see Sect. 2.2.1). As an illustrative
example, Fig. 5.9 (a) shows the RSM of (204) reflexion of both SrTiO3 substrate and
60-nm (Bi0.9La0.1)2NiMnO6 film (grown in the optimised deposition conditions for
single-phase stabilisation). As qperp = l/c = 4/c [see Eq. 2.6], where c is the out-of-plane
lattice parameter, (Bi0.9La0.1)2NiMnO6 peak is found at higher values of qperp than that of
the substrate, as (Bi0.9La0.1)2NiMnO6 unit cell is smaller than that of the SrTiO3 (Fig.
5.9). Instead, qparallel of (204) (Bi0.9La0.1)2NiMnO6 reflexion is found to be coincident
with that of the substrate (indicated by the two guide-to-eye dashed lines corresponding
to Kα1 and Kα2). As qparallel = h/a = 2/a [see Eq. 2.6], where a is the in-plane lattice
parameter, it means that (Bi0.9La0.1)2NiMnO6 in-plane lattice parameter adopts the value
of the SrTiO3 lattice parameter (3.905 Å).
169
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.9 – Reciprocal space map
of the (204) reflexion of SrTiO3
and (204) reflexion of a 60-nm
(a) 100-nm (b) and 130-nm (c)
(Bi0.9La0.1)2NiMnO6
(BLNMO)
thin film (grown at 620ºC and 0.5
mbar of O2). The red dashed and
blue dashed line (Kα1 and Kα2,
respectively)
are
guide-to-eye
lines showing that the in-plane
lattice parameter of BLNMO is
coincident with the SrTiO3 lattice
parameter.
170
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Exploring RSM for thicker films [Fig. 5.9 (b) and (c)], no relaxation is observed,
i.e. qparallel of (204) (Bi0.9La0.1)2NiMnO6 reflexion and (204) SrTiO3 reflexion are still
coincident. This is likely due to the small mismatch between lattice parameters of
(Bi0.9La0.1)2NiMnO6 and SrTiO3 (see table 5.1). Thus, (Bi0.9La0.1)2NiMnO6 films grow
coherently on SrTiO3 substrates up to 130 nm of thickness (lower bound), adopting the
SrTiO3 lattice parameter as the in-plane lattice parameter. Hence, (Bi0.9La0.1)2NiMnO6
films are tensile strained, about 0.72%, defined as following:
strain =
a film − abulk
abulk
= 0.72%
(5.1)
where afilm and abulk are the film in-plane lattice parameter and the bulk pseudocubic
lattice parameter of (Bi0.9La0.1)2NiMnO6, respectively.
Fig. 5.10 – Thickness dependence of in-plane (solid square symbols) and out-of-plane
(open square symbols) lattice parameters of (Bi0.9La0.1)2NiMnO6 films (grown at 620ºC
and 0.5 mbar of O2 pressure). Upper dashed line indicates the lattice parameter of
SrTiO3 (3.905 Å), whereas bottom dashed line indicates the average value of the out-ofplane lattice parameter (3.871 Å).
171
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
In Fig. 5.10 (left axis) in-plane lattice parameter computed by means of the RSM as
a function of (Bi0.9La0.1)2NiMnO6 thickness is depicted, which is roughly constant
around the value of SrTiO3 lattice parameter. The out-of-plane lattice parameter,
determined by RSM [Fig. 5.10 (right axis)] is roughly constant along thickness (~ 3.87
Å), as expected when no relaxation takes place. Note that the (Bi0.9La0.1)2NiMnO6
lattice parameters obtained by RSM are computed from Δqparallel and Δqperp between
q( 204) of (Bi0.9La0.1)2NiMnO6 and q( 204) of SrTiO3, using that of SrTiO3 as a reference,
with lattice parameter (3.905 Å), accounting for the experimental error (see Appendix
A).
Thus, the unit cell volume of (Bi0.9La0.1)2NiMnO6 films [Vu.c = a2·c; as
(Bi0.9La0.1)2NiMnO6 film have a tetragonal structure] is maintained constant along
thickness. However, contrary to the common assumption that epitaxial strain preserves
the bulk unit cell volume, (Bi0.9La0.1)2NiMnO6 films possess a noticeable larger unit cell
volume (~59.03 Å3) than that of the bulk (58.29 Å3). Yet this is a rather common result
in many epitaxial films.
On the other hand, the out-of-plane lattice parameter of (Bi0.9La0.1)2NiMnO6 films
can also be computed by the symmetric XRD reflexions (Fig. 5.11), i.e. from the θ/2θ
XRD scans, as described in Sect. 2.2.1. In the symmetric XRD reflexions only the
crystallographic planes (hkl) that are parallel to the surface of the film are allowed to
diffract, in our case the (00l) family of planes. Hence, the interplanar distance of this
family of planes are directly related to the out-of-plane lattice parameter (denoted as c):
d00l = c/l (see Appendix A). Note that in order to account for the instrumental error, the
2θ position of the (00l) XRD reflexions of SrTiO3 were also computed and used the
lattice parameter of SrTiO3 (3.905 Å) as a reference (see Appendix A). Fig. 5.11 (a)
shows the out-of-plane lattice parameter, computed by the symmetric XRD patterns, of
(Bi0.9La0.1)2NiMnO6 films grown at different temperatures when the oxygen pressure
during growth is maintained constant at 0.5 mbar. Despite the fact that at lower and
higher temperatures than 620ºC spurious phases are formed (NiO) together with
(Bi0.9La0.1)2NiMnO6 phase (Fig. 5.1), the out-of-plane lattice parameter of
(Bi0.9La0.1)2NiMnO6 phase are roughly constant (~3.87 Å) along the temperature range.
This contrasts with BiMnO3 phase (see Sect. 4.1.1), in which the out-of-plane lattice
172
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
parameter monotonously reduces upon deposition temperature, associated with an
increasing presence of Bi vacancies.
Fig. 5.11 – Out-of-plane
lattice
parameter
(Bi0.9La0.1)2NiMnO6
of
thin
films as a function: (a) the
deposition temperature (O2
pressure maintained at 0.5
mbar); (b) the O2 pressure
during the thin film growth
(temperature maintained at
620ºC); and (c) thickness
(grown at 620ºC and 0.5
mbar of O2 pressure).
173
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
The dependence of the out-of-plane lattice parameter on the oxygen pressure during
the thin film growth is also negligible [Fig. 5.11 (b)], in which a value around 3.87 Å is
also recorded in the whole range (from 0.3 mbar to 0.6 mbar). In addition, thickness, t,
dependence of the out-of-plane lattice parameter, c(t), was also assessed by the
symmetric (00l) XRD reflexion [Fig. 5.11 (c)]. As shown, c(t) remains invariant (~3.87
Å) along thickness, in agreement with the out-of-plane lattice parameter extracted from
the reciprocal space maps, which gives an additional evidence of the lack of relaxation
process of (Bi0.9La0.1)2NiMnO6 films grown on SrTiO3.
Hence, as a conclusion, (Bi0.9La0.1)2NiMnO6 films grow fully tensile strained on
SrTiO3 substrates, thus, with a lattice parameter (in-plane) around 3.905 Å, and c lattice
parameter (out-of-plane) is found around 3.87 Å.
5.2.3 Microstructure characterisation by
transmission electron microscopy
Fig. 5.12 – (a) General view of cross-section TEM image of (Bi0.9La0.1)2NiMnO6
(BLNMO) film. STO stands for SrTiO3 substrate. The measured thickness is in good
agreement with that obtained by X-ray reflectivity (b), using the expression 2.10
deduced in Ch. 2, in which the slope of the sin2θm versus m2 corresponds to [λ/(2·t)]2,
where θm and m are the θ position of the minimum of order m; and t and λ are the film
thickness and the wavelength of Kα of Cu, respectively.
174
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Transmission electron microscopy (TEM) was used to assess the substrate-film
interface, as well as the homogeneity of the film, the crystal quality and the epitaxial
growth of the film. TEM samples were prepared in cross-section geometry by focused
ion beam, as explained in Sect. 2.2.2 (Ch. 2). The sample investigated was a 68-nm
(Bi0.9La0.1)2NiMnO6 film grown at the optimised deposition conditions for single phase
stabilisation (620ºC and 0.5 mbar of O2 pressure). The thickness determined by TEM
[Fig. 5.12 (a)] is in close agreement with that extracted by X-Ray reflectivity [Fig. 5.12
(b)].
Fig. 5.13 – Cross-section along [100] direction TEM image of BLNMO and SrTiO3
(STO).
Low magnification TEM image is shown in Fig. 5.13, which evidences the
homogeneity of the film along thickness.
High-resolution TEM (HRTEM) images [Fig. 5.14 (a) and (b)] were adquired in
order to obtain information about the microstructure and crystallographic features of
(Bi0.9La0.1)2NiMnO6 films. Accordingly, high crystalline quality can be appreciated, in
which no misfit dislocations are observed, as expected for a fully strained film with no
relaxation according to the XRD results. The high crystal quality is also in agreement
with the sharp rocking curves of (Bi0.9La0.1)2NiMnO6 films compared with that of the
substrate, as assessed by XRD measurements (Sect 5.2.1). Additionaly, Fig. 5.14 (b)
175
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
shows that the (Bi0.9La0.1)2NiMnO6/SrTiO3 interface is strikingly sharp, which indicates
no cationic interdifusion across the interface, as will be deeper discussed in Sect. 5.3., in
composition analysis of (Bi0.9La0.1)2NiMnO6 films.
Fig. 5.14 – (a) HRTEM image of (Bi0.9La0.1)2NiMnO6 (BLNMO) film prepared in crosssection geometry along [100] direction. (b) Higher magnification HRTEM image of
BLNMO/SrTiO3 interface.
Fast Fourier Transmforms (FFTs) of selected areas of the HRTEM images were
computed in order to assess the periodicity of the crystal lattice. According to the FFTs
of selected areas of substrate and film [Fig. 5.15 (b) and (c), respectively, from the
selected areas marked by a green and blue square, respectively, in Fig. 5.15 (a)] the
crystallographic directions of both substrate and film are coincident, accomplishing the
epitaxial relationship [100](Bi0.9La0.1)2NiMnO6(001)//[100]SrTiO3(001), in agreement
with XRD measurements. Thus, (Bi0.9La0.1)2NiMnO6 films grow well adapted on
SrTiO3 substrates.
To sum up, TEM characterisation, apart from indicating (Bi0.9La0.1)2NiMnO6 film
being defect-free and a sharp interface between film and SrTiO3 substrate, bears out the
high crystal quality of (Bi0.9La0.1)2NiMnO6 films and the epitaxial relationship
[100](Bi0.9La0.1)2NiMnO6(001)//[100]SrTiO3(001), as proved by XRD measurements.
176
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
(b)
(a)
SrTiO3
(010)
(011)
(001)
SrTiO3 [100]
(c)
(010)
(011)
(001)
BLNMO
BLNMO [100]
Fig. 5.15 – (a) HRTEM image of (Bi0.9La0.1)2NiMnO6 (BLNMO) and SrTiO3 substrate
prepared in cross-section geometry along [100] direction. The green (blue) square
mark signals the selected area of the substrate (film) where FFT is taken. FFT of
SrTiO3 substrate (b) and BLNMO film (c).
5.2.4 B-site order
In double-perovskite Bi2NiMnO6, the B-site order, i.e. how the Ni2+ and Mn4+
cations are placed in the structure regarding one another, is strongly influential on the
magnetic properties. Whereas Ni – O – Ni and Mn – O – Mn bonds give rise to
antiferromagnetic superexchange interaction, Ni – O – Mn bond give rise to
ferromagnetic superexchange interaction (see Sect. 1.2.5).
Thus, for a long-range ferromagnetic interaction, Ni and Mn cations are required to
be located alternatively along the [100], [010] and [001] crystallographic directions
(Fig. 5.16). In this work long-range B-site order is defined as the fulfilment of this
periodicity, also known as rock-salt structure of the double-perovskite [5, 9, 10]. This
periodicity results in the alternation of Ni-planes and Mn-planes along the [111]
direction (along the eight equivalent directions: [1-11], [11-1], [-111], [1-1-1], [-11-1],
[-1-11], [-1-1-1], [111]), as shown in Fig. 2.13 in Ch. 2. As a consequence, occurrence
of the (1/2 1/2 1/2) superstructure XRD reflexion should be expected. However, as the
177
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
atomic scattering factor of Ni2+ and Mn4+ are very similar, the superstructure XRD
reflexion in Bi2NiMnO6 is very weak. Note that should B cations be identical, like in
SrTiO3, systematic XRD cancellation occurs and no superstructure XRD reflexion is to
be observed, so that the larger the difference in the atomic scattering factor of the B
cations, the higher the intensity of the superstructure XRD reflexion.
Fig. 5.16 – Scheme of the double-perovskite structure in the rock-salt configuration
In order to observe this weak superstructure XRD reflexion, first X-ray diffraction
using synchrotron radiation was used, which provides an intense source of X-rays,
allowing detecting the weak XRD reflexion (for experimental details see Sect. 2.4 of
Ch. 2). Second, electron diffraction using TEM and computing FFT’s HRTEM images
were used in order to corroborate the synchrotron XRD results. The samples used for
the B-site order characterisation were those grown at the optimal deposition conditions
for single-phase stabilisation, i.e. at 620ºC and 0.5 mbar of O2 pressure.
Fig. 5.17 (a) and (b) depict θ/2θ synchrotron XRD scan around (111) and (1/2 1/2
1/2) (Bi0.9La0.1)2NiMnO6 reflexions, respectively, of a 100-nm film. Due to the similar
lattice parameters of (Bi0.9La0.1)2NiMnO6 and SrTiO3, Fig. 5.17 (a) shows the
contribution of the fundamental perovskite (111) reflexion of both film and substrate
(2θfilm ~ 32.62º and 2θsusbtrate ~ 32.59º, respectively). In contrast, as superstructure order
is absent in SrTiO3, the sole contribution observed in Fig. 5.17 (b) should correspond to
(1/2 1/2 1/2) (Bi0.9La0.1)2NiMnO6 XRD reflexion. Indeed, the peak appears around 2θ ~
16.14º, as expected, since, according to the Bragg’s law [Eq. 2.1, Ch. 2], it must fulfil
178
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
the relation sin(θ(1/2
1/2 1/2))
= (1/2)·sin(θ(111)), given the fact that the distance between
(111) planes and (1/2 1/2 1/2) planes is d(1/2 1/2 1/2) = 2·d(111). Therefore, Fig. 5.17 (b)
unequivocally reveals the long-range B-site order of (Bi0.9La0.1)2NiMnO6 thin films.
Fig. 5.17 – (a) θ/2θ synchrotron XRD scan around the fundamental perovskite (111)
reflexion of (Bi0.9La0.1)2NiMnO6 (BLNMO) and SrTiO3. (b) θ/2θ synchrotron XRD scan
around the (1/2 1/2 1/2) superstructure reflexion of BLNMO. The diffraction intensity
peaks were fitted using Gaussian functions.
Fig. 5.18 – HRTEM image of BLNMO and SrTiO3 in cross-section geometry prepared
along ⎡⎣1 10 ⎤⎦ direction.
In order to detect the superstructure diffraction peaks by TEM, cross sections were
to be prepared along the [1-10] zone axis (instead of the common [100] zone axis as
179
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
prepared in Sect. 5.2.3) as this cross-section geometry enables the observation of the
reflexions related to the {111} crystallographic planes. Fig. 5.18 shows the HRTEM
image of a cross-section prepared along [1-10] zone axis of a 68-nm
(Bi0.9La0.1)2NiMnO6 film, showing both the film and the substrate, in which the high
crystal quality and sharp interface between (Bi0.9La0.1)2NiMnO6 and SrTiO3 are
appreciated, corroborating the results obtained for cross-sections prepared along [100]
crystallographic direction (Sect. 5.2.3).
Fig. 5.19 – (a) HRTEM image of cross-section prepared along the ⎡⎣1 10 ⎤⎦ zone axis of
(Bi0.9La0.1)2NiMnO6 (BLNMO) films on SrTiO3. (b) FFT of the selected area (b) red
square (c) blue square (d) green square taken from the HRTEM image. A1, A2 and A3
spots corresponds to (001), (111) and (110) crystallographic planes, respectively. The
extra periodicity is signalled by B1.
180
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.19 (b) depicts the FFT of a selected area of pure SrTiO3 [marked as a red
square in HRTEM image, Fig. 5.19 (a)], which shows the spots A1, A2 and A3
corresponding to the (001), (111) and (110) planes, respectively. However, when FFT is
are computed from selected areas in which (Bi0.9La0.1)2NiMnO6 film is included [Fig.
5.19 (c) and (d), from the selected areas marked by a blue and green square,
respectively, in HRTEM image Fig. 5.19 (a)], apart from the A spots which corresponds
to the fundamental perovskite planes (corroborating the epitaxial growth of
(Bi0.9La0.1)2NiMnO6 film) additional weak spots are found along the [111] direction,
marked as B1. These additional spots point out to an extra periodicity along the [111]
direction, which is compatible with the aforementioned B-site order. Moreover, the fact
that the additional spots appear as early as the first monolayers [Fig. 5.19 (c)] proves the
existence of the superstructure in (Bi0.9La0.1)2NiMnO6 films in the initial steps of the
growth process.
To bear out the results of the computed FFT’s of the HRTEM images, real
diffraction is performed by selected area electron diffraction (SAED), equipped in
TEM, on cross-sections prepared along the [1-10], enabling {111} planes to diffract.
Nonetheless, due to the small thickness of (Bi0.9La0.1)2NiMnO6 film (68 nm), SAED
patterns of only (Bi0.9La0.1)2NiMnO6 regions were no possible to be performed. Thus, in
order to compare the electron diffraction patterns between (Bi0.9La0.1)2NiMnO6 and
SrTiO3, SAED patterns were recorded in a region where only SrTiO3 substrate is found
and in a region where (Bi0.9La0.1)2NiMnO6 film is included, with SrTiO3 substrate
contribution. Fig. 5.20 (a) and (b) shows SAED patterns of pure SrTiO3 substrate, in
which only the diffraction of the fundamental perovskite planes are found, identifying
A1, A2 and A3 spots with the (001), (111) and (110) crystallographic planes,
respectively, as found in the FFT’s. In contrast, SAED patterns in which
(Bi0.9La0.1)2NiMnO6 film contribution is present [Fig. 5.20 (c) and (d)] an extra
periodicity along the [111] direction is observed, marked with green circles, which we
identify as the (1/2 1/2 1/2) superstructure diffraction peaks. Indeed, the value of the
crystallographic interplanar distance of the planes corresponding to the extra periodicity
(green circles) is about 0.45 nm (determined by the spot B1, see table 5.4), which is in
close agreement with the expected interplanar distance of the (1/2 1/2 1/2)
superstructure planes:
181
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
d hkl =
1
⇒ d 1 1 1 = 0.4496 nm
h + k 2 l2
222
+ 2
a
c
2
(5.2)
where a and c is the in-plane and the out-of-plane lattice parameter of
(Bi0.9La0.1)2NiMnO6 film.
Fig. 5.20 – (a) Selected area electron diffraction pattern of pure SrTiO3 along the
⎡⎣1 10 ⎤⎦ zone axis. (b) Zoom of (a). (c) Selected area electron diffraction pattern of
contribution of both SrTiO3 and (Bi0.9La0.1)2NiMnO6 film along the ⎡⎣1 10 ⎤⎦ zone axis. (d)
Zoom of (c). A1, A2 and A3 spots correspond to the diffraction of (001), (111) and (110)
crystallographic planes. Encircled spots correspond to the diffraction of superstructure
planes.
As a conclusion, despite the high temperature usually required for the formation of
the rock-salt structure in double-perovskite thin films, like La2CuSnO6, Sr2FeMoO6,
Sr2CrReO6 or La2CoMnO6 [10 – 12], experimental results evidence that long-range Bsite order can be achieved in (Bi0.9La0.1)2NiMnO6 films under relatively low deposition
182
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
temperatures of thin film growth (around 620ºC). On the other hand, the randomly
distribution of Bi3+ and La3+ cations at the A-site in (Bi0.9La0.1)2NiMnO6 films does not
seem to affect the arrangement of the B cations.
Spot
Crystallographic plane
Distance (nm)
A1
(001)
0.39
A2
(111)
0.23
A3
(110)
0.28
B1
(1/2 1/2 1/2)
0.45
Table 5.4 – Distance between the crystallographic planes of selected diffraction spots
of Fig. 4.21.
5.2.5 Surface topography
Most of the applications in which a multilayer structure of nanometric films is
required (tunnel junctions, spin valves, etc) the surface morphology plays an essential
role. In addition, studying the surface topography contributes to the understanding of
the growth mechanism of (Bi0.9La0.1)2NiMnO6 thin films on SrTiO3, which may be
extended to other similar substrates in perovskite structure with similar lattice
parameters. AFM was used in the characterisation of surface topography, as explained
in Sect. 2.3.2. In this study, only single-phase samples, i.e. those grown at 620ºC, were
characterised.
(Bi0.9La0.1)2NiMnO6 thin films grown on SrTiO3 substrates exhibit a different
morphology compared to their counterpart single-perovskite BiMnO3 grown also on the
same substrate (see Sect. 4.2.3). In the present case, the substrate steps and terraces are
maintained when the film is grown, as shown in Fig. 5.21 (a). This is indicative of a 2D
growth mode, which contrasts with the 3D growth mode found for BiMnO3 thin films
(Sect. 4.2.3). The height profile [Fig. 5.21 (c)] along the marked line in Fig. 5.21 (a)
indicates steps of height between 1 and 2 (Bi0.9La0.1)2NiMnO6 unit cells. Additionally,
some 2D island can be found on the terraces, which might be pointing to a certain
degree of a layer-by-layer growth mechanism, though with a likely coexistence of a
step-flow growth mode. A systematic study of the surface morphology at the earlier
183
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
stages of the growth process was not carried out, which would contribute to discern
whether the adatoms have a preferential diffusion toward the step edges (step-flow) or
nucleate as 2D islands on the terraces (layer-by-layer). Step meandering can also be
observed [Fig. 5.21 (a)]. Steps usually introduce Ehrlich–Schwoebel terrace potentials
which oppose adatom to hop from the upper terrace to the bottom one, creating step
bunching [13, 14]. However, these step mounds might not be uniform along the step
edges due to the presence of kinks or irregularities. In a step-flow growth mode, this
fact can cause different adatom diffusion rates over the edges, which may explain the
observed meandering.
5.42 nm
9.73 nm
0.00 Å
0.00 Å
(c)
Fig. 5.21 – AFM topographic images of (Bi0.9La0.1)2NiMnO6 thin films grown on (001)oriented SrTiO3 substrates of thickness (a) 68 nm (rsm = 0.35 nm) (b) 125 nm (rsm =
0.6 nm). (c) Height profile corresponded to the marked line in AFM image of the 68-nm
thick film (a). [Note the miscut angle was computed and subtracted from the height
profile]
184
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
For films thinner than 80 nm a 2D growth mode is found; however, for the thickest
samples a 3D growth mode is observed [Fig. 5.21 (b)]], indicating that a transition from
2D to 3D is occurring at some critical thickness between 80 and 110 nm when the film
continues growing.
Due to the fact that 2D growth mode is achieved in (Bi0.9La0.1)2NiMnO6 thin films
thinner than some critical thickness very flat surfaces are obtained, with root-meansquare (rsm) surface roughness of less than 0.5 nm. Yet for the thickest films in which a
3D growth mode is starting to dominate, the recorded rsm surface roughness values are
still low, of less than 1 nm, which evidences the smooth surfaces obtained in
(Bi0.9La0.1)2NiMnO6 thin films grown on SrTiO3 up to large values of thickness.
5.3 Chemical analysis
5.3.1 Composition analysis
The presence of highly volatile species, i.e. Bi, greatly hampers synthesising
stoichiometric Bi-based multiferroic thin films, as observed in BiMnO3 thin films (see
Sect. 4.1). Although high substrate temperatures is required when it comes to forming
single-phase and high-quality crystalline samples of Bi-based metastable multiferroics,
it is not a free deposition parameter due to the fact that Bi-deficiency starts to be
significant at temperatures as low as 640ºC, as found in BiMnO3 (see Sect. 4.1.1). Here,
a thorough study of the substrate temperature dependence of the Bi content in
(Bi0.9La0.1)2NiMnO6 thin films was not carried out, yet a similar behaviour with
BiMnO3 thin films is expected to be found as XRD results (Sect. 5.1) shows the
presence of spurious phases above 640ºC of synthesising temperature, much likely
related to the increasing Bi-deficiency. Single-phase samples, i.e. those grown at the
intermediate temperatures around 620ºC (see sect. 5.1) were analysed by EELS, as
explained in Sect. 2.4.3.
185
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.22 – (a) HAADF general image of a 68-nm (Bi0.9La0.1)2NiMnO6 film on SrTiO3
substrate. The purple line indicates the path on which EELS compositional profiles
were taken. (b) Elemental quantification obtained by EELS along thickness (subjected
to a relative error of 5 %). The dashed line indicates the interface between film and
substrate. (c) Cationic composition ratio of [Bi]/[Mn] along the film thickness. (d)
Cationic composition ratio of [Ni]/[Mn] along the film thickness.
EELS compositional profiles obtained in [100] cross sectional TEM lamellas were
acquired in perpendicular direction to (Bi0.9La0.1)2NiMnO6/SrTiO3 interface following
the path marked in Fig. 5.22 (a). They have been determined from general spectra, in
the low-loss (between 40 and 470 eV) and core-loss (between 420 eV and 930 eV)
regions. The concentration of the different species is depicted in Fig. 5.23 (b), which,
accordingly, no ionic interdiffusion across the interface is found. Neither does there
seem to be noticeable cationic segregations along the film thickness, as it occurs with
La also located at the A-site in (La,Ca)MnO3 perovskite thin films grown on SrTiO3
(001) [15]. Importantly enough, despite the high volatility of Bi, the film composition is
186
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
highly stoichiometric and homogeneous, bearing out 620ºC as an appropriate grown
temperature, i.e. high enough to obtain single phase samples and low enough to prevent
large Bi desorption during deposition. Thus, the Bi content normalized by Mn content is
around the nominal value: 1.8, as shown in Fig. 5.22 (c). On the other hand, the
compositional relationship between Ni and Mn is, as expected, 1:1 [Fig. 5.22 (d)].
5.3.2 Oxidation state of B-cations
As explained in the Ch.1, the oxidation state of Ni and Mn plays a crucial role in the
magnetic properties as much as the long-range B-site order in a rock-salt configuration.
In (Bi,La)2NiMnO6 two different configuration of the valence state of the B-cations are
enabled, either Ni3+/Mn3+ or Ni2+/Mn4+, being only the latter the appropriate for
building up superexchange ferromagnetic paths, i.e. Ni2+ – O – Mn4+ (see 1.2.5). Apart
from the different possible configuration, the presence of oxygen vacancies may also
alter the oxidation state of the B-cations, which, in turn, the magnetic properties of
(Bi,La)2NiMnO6 thin films. The valence of the B-cations was studied by EELS and XPS
(see Sect. 2.4.1 and 2.4.3) of single-phase samples grown at 620ºC.
EELS spectra in the 400 to 750 eV energy-loss range was recorded, where Mn L2,3
edges take place. These peaks are known to be related to the formal valence of
manganese ions [15, 16], as Mn L2 and L3 peak position are shifted to higher energies
on decreasing the occupancy of d orbitals, whereas L3/L2 intensity ratio decreases when
the orbital configuration varies from d5 to d0 or d10. Thus, for Mn4+, i.e. with an orbital
configurations d3, L3 edge is expected to be shifted to higher energies than that of Mn3+
(d4 of orbital configuration) and L3/L2 intensity ratio is to be found smaller for Mn4+
with regard to Mn3+. The expected intensity ratios L3/L2 and energy positions of L3
edges corresponding to the different oxidation states of Mn ions are depicted in dotted
lines in Fig. 5.23 (a) and (b), respectively. The experimental collected data (solid square
symbols in Fig. 5.23), determined by using a home-made software package
MANGANITAS [15, 17, 18], are plotted in Fig. 5.23 (solid square symbols). Results
evidence the homogeneity of Mn4+ within (Bi0.9La0.1)2NiMnO6 thin films, without traces
of Mn3+ or Mn2+ indicating that the films are fully oxidized. Likewise, the Ni oxidation
state has been assessed by Ni L2 and L3 edges, which occur at 872 and 855 eV,
respectively. The determined fine structure of these L2,3 edges corresponds to the
187
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
divalent oxidation state [19], as expected taken into account that the valence of Mn is
4+.
Fig. 5.23 – Mn L3/L2 intensity ratio (a) and L3 peak onset (b) obtained along thickness
of a 68-nm (Bi0.9La0.1)2NiMnO6 thin film [EELS profiles obtained along the marked line
in Fig. 5.22 (a)]. L3/L2 intensity ratio is subjected to 5% of relative error. L3 peak onset
is subjected to a ± 0.4 eV error.
On the other hand, as a complementary technique, XPS was also used to obtain the
valence state of Mn of (Bi0.9La0.1)2NiMnO6 thin films from the Mn 3s photelectron
spectra, as explained in Sect. 2.4.1. Nonetheless, this technique is very surface sensitive,
so that only the top ~2 nm of the film can be analysed. In order to perform XPS analysis
along thickness, XPS is complemented by ion sputtering which allows obtaining XPS
spectra at different depth by eroding the film. However, ion bombarding is a quite
aggressive technique which may greatly alter the compositional ratios, but especially
counter-productive is the fact that it modifies the chemical bonds completely giving rise
188
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
to misleading information about the oxidation state of the species. Therefore no ion
bombarding was used to characterise the valence of the B cations.
Fig. 5.24 – Mn 3s photoemission spectra of 125-nm (Bi0.9La0.1)2NiMnO6 thin film grown
on SrTiO3 (001).
XPS measurements were performed on as-grown (Bi0.9La0.1)2NiMnO6 thin films on
SrTiO3 substrates and recorded the Mn 3s photoelectron spectra, which takes place
between 90 and 80 eV. The splitting of the Mn 3s into two peaks in the photoelectron
spectra (see Fig. 5.24) is due to the exchange coupling between the 3s holes and 3d
electrons and hence it is closely related to the valence of Mn (the 3d orbitals filling
indicates the oxidation state of Mn) [20, 21]. Specifically, the difference in energy of
the Mn 3s peaks monotonically decreases as the oxidation state of Mn increases from
2+ to 4+ (see Fig. 2.16, Sect. 2.4.1) [20]. The two peaks of Mn 3s photoelectron spectra
were fitted by two Gaussian functions as plotted in Fig. 5.24, from which the splitting in
energy (≡ΔE3s) was computed.
As the oxygen pressure during thin film growth is one of the main sources of the
formation of oxygen vacancies in many oxide films [22 – 26], which would lead to
lowering of the oxidation state of the cations, different (Bi0.9La0.1)2NiMnO6 samples
grown at different O2 pressures were analysed by XPS. The computed ΔE3s of Mn 3s
spectra as a function of the oxygen pressure during growth is shown in Fig. 5.25. The
expected ΔE3s for Mn2+, Mn3+ and Mn4+ is depicted as dashed lines. Accordingly, in the
range of oxygen pressures used in this work (0.3 – 0.6 mbar) no variation in the
189
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
oxidation state of Mn is found, which remains 4+ irrespectively. On the other hand, Mn
3s spectra were also recorded for different thick films grown at 0.5 mbar of O2 pressure,
the computed ΔE3s of which is plotted in Fig. 5.26. Likewise the previous case, at any
thickness only the presence of Mn4+ is found.
Fig. 5.25 – Mn 3s energy splitting of 125-nm (Bi0.9La0.1)2NiMnO6 thin films grown at
620ºC at different O2 pressures on SrTiO3 (001). The dashed lines indicate the expected
Mn 3s energy splitting of different oxidation states of Mn (extracted from Ref. 20).
Fig. 5.26 – Mn 3s energy splitting of (Bi0.9La0.1)2NiMnO6 thin films of different thickness
grown at 0.5 mbar of O2 pressure on SrTiO3 (001). The dashed lines indicate the
expected Mn 3s energy splitting of different oxidation states of Mn (extracted from Ref.
20).
190
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
To conclude, although XPS measurements are only sensitive to the top layers of the
films, EELS has corroborated the homogeneity of the tetravalent state of Mn along
thickness. Importantly enough, the oxygen pressure during thin film growth, which
tends to be a crucial thin film deposition parameter in terms of oxygen vacancies
formation, does not play a significant role in the oxidation state of Mn, which remains
invariant 4+ (note that the valence state of Ni is never to be 1+ in order to compensate
the electric equilibrium in presence of oxygen vacancies). Hence, (Bi0.9 La0.1)2NiMnO6
thin films are expected to be fully oxidised, within the sensitivity of EELS and XPS. It
is to be remarked, though, that the films were always cooled down under 1000 mbar of
O2 pressure after deposition, resulting in both preventing the formation of oxygen
vacancies during the cooling down process and oxygenating the film completely if it
was not yet. On the other hand, no deviation of the tetravalent state of Mn is found
when increasing the film thickness, pointing to an homogenous oxygenation along
thickness.
Interesting enough, as only the divalent and trivalent sate of Ni cations are
energetically favoured, the fact that only Mn4+ is found in (Bi0.9La0.1)2NiMnO6 thin
films rules out the presence of Ni3+, evidencing the highly desirable configuration of
Ni2+/Mn4+ of the B-cations in (Bi0.9 La0.1)2NiMnO6 thin films, which favours the
ferromagnetic interactions.
5.4 Magnetic properties
As explained in chapter 1, the magnetic order in (Bi0.9La0.1)2NiMnO6 arises from
the superexchange interaction of the magnetic ions, i.e. Ni and Mn, located at the B-site,
mediated by the adjacent oxygen anions. Nonetheless, the sign of the magnetic
superexchange interaction (whether it is ferromagnetic or antiferromagnetic) is strongly
dependent on the electronic configuration of the magnetic ions and their order at the Bsite. The results of previous sections (Sect. 5.3.2) give evidence for Ni and Mn cations
being divalent and tetravalent, respectively. Moreover, crystal structure data (Sect.
5.2.4) proves that Ni and Mn orders alternatively along [100], [010], [001] pseudocubic
directions in a rock-salt configuration (see Fig. 5.16), being Mn cations the first Bcation neighbours of each Ni cation and vice versa, separated just by the oxygen anions.
191
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Hence,
according
to
the
Kanamori-Goodenough
rules
[27],
ferromagnetic
superexchange interaction is expected along the 180º-bond-angle Ni2+(t2g6eg2, half-filled
eg orbitals) – O – Mn4+(t2g6eg0, empty eg orbitals). The long-range B-site order ensures a
long-range ferromagnetic coupling of the spins of Ni2+ and Mn4+, so that
(Bi0.9La0.1)2NiMnO6 thin films are expected to behave ferromagnetically.
Single-phase (Bi0.9La0.1)2NiMnO6 thin film samples grown at 620ºC and 0.5 mbar
of O2 mbar were used for the magnetic characterisation. The applied magnetic field, H,
has been applied along an in-plane direction. The large diamagnetic contribution of the
substrate SrTiO3 was removed from the raw data (see Appendix B). Magnetisation data
versus applied magnetic field, M(H), recorded at 10 K, is shown in Fig. 5.27, in which
an hysteretic M(H) behaviour can clearly be observed, proving the expected
ferromagnetic character of (Bi0.9La0.1)2NiMnO6 thin films. The magnetic remanence,
which can be appreciated in the inset of Fig. 5.27, is rather low indicating a small
magnetic anisotropy in the system.
The magnetisation measured at the highest applied magnetic field, 7 T, is around
3.5 μB/f.u. (Fig. 5.27), in close agreement with data reported for bulk
(Bi0.9La0.1)2NiMnO6 samples [MS (7 T, 5 K) ~ 3.6 μB/f.u)] [7], although neither do bulk
samples [7] nor do our thin films saturate at the highest magnetic field, but, instead, it
shows a gradual increase. For an ideal ferromagnetic coupling of the spins of Ni2+ (S =
1) and Mn4+ (S = 3/2), a saturated magnetisation of MS = 5 μB/f.u. is expected (see Sect.
1.2.5). Due to the lack of saturation of the M(H) of our (Bi0.9La0.1)2NiMnO6 thin films it
is elusive to determine their MS. Nonetheless, in the case of non-La-doped Bi2NiMnO6
samples, in which M(H) saturates at 4 T, a reduced MS is reported for both bulk samples
(MS ~ 4.1 μB/f.u) [5] and thin films (MS ~ 4.5 μB/f.u) [8].
192
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.27 – Magnetic field dependence of the magnetization of a 100-nm-thick
(Bi0.9La0.1)2NiMnO6 thin film. Bottom inset: Zoom of the low field region. The coercive
field is about 0.5 kOe.
One possible explanation of the probable reduced magnetisation of our films could
be the presence of some residual Mn3+ due to the formation of oxygen vacancies, as
Ni2+ – O – Mn3+ can give rise to antiferromagnetic superexchange interaction. Note that
Mn3+ contains one half-filled eg orbital, z2, in a Jahn-Teller distortion of the perovskite
(chapter 1), which couples antiferromagnetically with the half-filled eg orbitals of Ni2+
[27]. Still, this possibility is highly unlikely as Ni and Mn were proved to have an
oxidation state of 2+ and 4+ irrespective of the partial oxygen pressure during thin film
growth, indicating they were fully oxidised at any event (Sect. 5.3.2). Nonetheless, for
the sake of completeness, a set of samples grown at 0.5 mbar of O2 pressure were in-situ
annealed at 450ºC under 1000 mbar of O2 pressure after PLD deposition for different
annealing time lengths in order to ensure full oxidation. Yet M(H) data of the different
annealed samples (Fig. 5.28) shows no significant different behaviour, recording almost
the same saturated magnetisation, MS ~ 3.5 μB/f.u, hence evidencing the presence of
Ni2+ and Mn4+ solely.
193
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.28 – Magnetic field dependence of the magnetization of 100-nm-thick
(Bi0.9La0.1)2NiMnO6 thin films in-situ annealed for different periods of time at 450ºC
and 1000 mbar of O2 pressure.
Alternatively, the possible reduced magnetisation could be due to the presence of
some antisite defects, i.e. the presence of either Ni – O – Ni or Mn – O – Mn, and
antiphase boundaries, common defects in double perovskites structures [11, 28, 29],
which may account for both the hardness to saturation and the accompanying reduced
magnetization as found here. Yet it is worth remarking that M(H) of bulk solid solution
of (Bi1-xLax)2NiMnO6 samples, 0.1 ≤ x ≤ 0.4 [7], unlike non-La-doped Bi2NiMnO6
samples [5, 8], saturates gradually in a wide range of La-doping, without reaching
saturation at the highest applied magnetic fields (H = 7 T). Therefore, the distinct
length and angles of Ni – O – Mn bonds around A-site when occupied either by La or
Bi cations, absent in non-doped Bi2NiMnO6 samples, may also play a significant role in
the ferromagnetic properties.
194
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.29 – Temperature dependence of the magnetization of 100-nm-thick
(Bi0.9La0.1)2NiMnO6 thin film under an in-plane applied magnetic field of 1000 Oe. Note
that diamagnetic contribution was substracted from raw data (see Appendix B).
The temperature dependence of the magnetisation, M(T), of single-phase
(Bi0.9La0.1)2NiMnO6 thin films is exemplified in Fig. 5.29, in which the sample is cooled
down under an applied in-plane magnetic field of 1000 Oe. The ferromagnetic transition
temperature occurs at TFM ~ 100 K. This value is significant lower than bulk
(Bi0.9La0.1)2NiMnO6 samples (TFM ~ 150 K) [7]. Nonetheless, similarly, Bi2NiMnO6
thin films grown on (001)-oriented SrTiO3 substrates show a significant reduced Curie
temperature (TFM ~ 100 K) [8, 30] with regard to bulk Bi2NiMnO6 samples (TFM ~ 140
K) [5]. Hence, it seems reasonable to ascribe this reduced TFM to the epitaxial strain
exerted by the substrate, which imposed a different Ni – O – Mn bond length and angle
(and consequently different intensity of the magnetic interaction) comparing to bulk
samples with free-standing lattice parameters.
On the other hand, M(T) curve shows a rather broad transition temperature (Fig.
5.29), which might point out to some distribution of magnetic superexchange
interactions within the sample. This could be due to the presence of dissimilar cations at
the A-site, as mentioned before, which no doubt results in distinct length and angles of
195
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Ni – O – Mn bonds. However, very similar M(T) curves, with very broad magnetic
transitions temperatures, are reported for Bi2NiMnO6 thin films as well [8, 30], so that it
might be an intrinsic magnetic behavior of these compounds when grown as thin films.
In summary,
(Bi0.9La0.1)2NiMnO6
thin
films have
been proved
to
be
ferromagnetically ordered below 100 K, reaching a large magnetization value
(compared to other multiferroics oxides, see table 1.5 in Ch. 1) of 3.5 μB/f.u at 7 T (at
10 K), in agreement with bulk magnetization values, but significantly smaller than
expected (~ 5 μB/f.u.). Nonetheless, the Curie temperature is found to be smaller than
bulk specimens likely driven by the epitaxial strain imposed by the substrate.
5.5 Ferroelectric properties
5.5.1 Background
properties
of
the
ferroelectric
As explained in chapter 1, the non-centrosymmetric distortion of Bi2NiMnO6 arises
from the stereochemical activity of the lone-pare 6s2 electrons of Bi (see Fig. 1.5, Sect.
1.2.2), which shifts away from the centrosymmetric position generating an electric
dipole. Polar structure is a required condition for ferroelectricity to be established but,
yet, not a sufficient one. Ferroelectric order implies that spontaneous polarization
appears which should be switchable by applying an electric field. Therefore, to
definitive bear out the ferroelectric character it is necessary to measure either a
ferroelectric hysteresis loop, i.e. polarisation versus electric field curves, P(E), that is to
measure the ferroelectric domain switching current when reverse the polarisation in the
sample by applying an opposite electric field (see Sect. 3.3). Yet these experiments can
be greatly hampered by the poor resistive character of multiferroic compounds, which
can completely alter the measurement by the leakage current (see Sect. 3.3).
Temperature XRD data analysis of bulk Bi2 NiMnO6 samples [5] showed that the
crystal structure was not centrosymmetric (monoclinic C2) below 485 K (see Sect.
1.2.5). Above that temperature the structure was indexed as centrosymmetric
monoclinic P21/n, which was accompanied with a large dielectric anomaly around the
196
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
transition temperature. These are the typical signatures of a ferroelectric phase
transition, hence pointing to the highly likely possibility of this material to be
ferroelectric below 485 K. On the other hand, La-doped Bi2NiMnO6 bulk samples were
also proved to be equivalently non-centrosymmetric for lower values of La contents, i.e.
less than 20% [7]. Yet neither ferroelectric hysteresis loop nor ferroelectric domain
switching current was measured in either case, which might be due to the likely leaky
character of (Bi,La)2NiMnO6 samples or the high voltages required for switching the
ferroelectric domains in bulk samples. Note that the applied electric field, E, as a result
of the applied voltage, V, in the common ferroelectric testing set-up parallel-plate
capacitor (sect. 3.1) scales as the inverse of the electrodes separation, d, i.e. E = V/d.
This distance is generally large in bulk specimens, hence giving rise to insufficient
electric fields for switching the ferroelectric domains.
The first, and only, reported ferroelectric hysteresis loop was performed on
Bi2NiMnO6 thin films at 7 K [8]. However, this hysteresis loop was far from being a
robust ferroelectric proof as the reported P(E) curve showed a negative slope at high
positive E fields or a positive slope at high negative E fields, which would indicate an
unphysical meaning negative dielectric permittivity, εr, as P = ε0(εr – 1)E (where bold
notation of P and E denotes their vector character and εr is a tensor).
Therefore, although (Bi1-xLax)2NiMnO6, x ≤ 0.2, compounds are promising
candidates to be multiferroic, their ferroelectric character remained still to be
unravelled.
5.5.2 Electric characterisation
ferroelectric properties
For
the
electric
characterisation
of
the
ferroelectric
of
the
properties
of
(Bi0.9La0.1)2NiMnO6 thin films, the parallel-plate capacitor configuration (see Fig. 3.1
and 3.2, Ch. 3) was used, i.e. Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 sandwich-capacitors
were fabricated (see Sect. 3.1). The thickness of the sample batch used was comprised
between 100 and 110 nm. The deposition conditions of (Bi0.9La0.1)2NiMnO6 thin films
were the optimised ones for single-phase formation, i.e. at 620ºC and 0.5 mbar of O2
pressure. The electric field was applied from top to top Pt electrodes (see Sect. 3.1),
197
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
which entails measuring two identical capacitors or equivalently a unique capacitor with
2t electrode-separation, where t is the film thickness. Hence, the applied electric field,
E, on the sample was computed by E = V/(2t), where V is the applied voltage. On the
following, for the sake of simplicity, P and E are going to be considered onedimensional, but actually what is measured in our experimental set-up (see Sect. 3.1) is
the out-of-plane Pi component of P that has the same direction as the applied electric
field E.
As (Bi0.9La0.1)2NiMnO6 thin films show a clear leaky behaviour, as it will be
analysed in Sect. 5.6, the so-called Positive-Up-Negative-Down (PUND) technique
(Fig. 3.16, Ch. 3) was used to measure the ferroelectric domain switching current (see
Sect. 3.3). PUND measurements were performed at 5 K closely to the accessible lowest
temperatures in the Physical Properties Measurement System (PPMS) (see Sect. 2.5.3)
in order to reduce as much as possible the conductive current. Note that the resistivity of
these compounds decreases exponentially on increasing temperature because of its
semiconductor character (as be discussed in sect. 5.6).
Fig. 5.30 shows the current versus time (~voltage) recorded in each triangular
voltage pulse (rise time of 25 μs, equivalent to 10 kHz) of the PUND measurement
(inset of Fig. 5.30). Whereas the current resulting from P and N pulses (labelled with P
and N in Fig. 5.30) contains the overall current (i.e. IFE + Iε + Ileakage, see Sect. 3.3), that
resulting from U and D pulses (labelled with U and D in Fig. 5.30) only contains the
non-ferroelectric part (i.e. Iε + Ileakage, see Sect. 3.3) as the sample is already polarised.
Thus, by subtracting the current from the U pulse from that of the P pulse (and similarly
D from N) we only obtain the current related to the switch of the ferroelectric domains,
IFE. The two current peaks that appear in P and N curves, absent in U and D curves,
unequivocally reveal the ferroelectric character of (Bi0.9La0.1)2NiMnO6 films.
198
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.30 – PUND measurement performed on Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3
capacitors at 5 K. Inset: Scheme of the PUND measurement.
As the triangular voltage pulses are linearly related to the rise time of the pulse,
current versus voltage, I(V) curves, can be computed. Once subtracted the nonferroelectric contributions, i.e. Iε + Ileakage, IFE(V) curves (Fig. 5.31 left axis) is extracted,
or equivalently, as a function of the applied electric field, E, as E = V/(2t). As shown,
the ferroelectric peaks can clearer be observed. The coercive field, Ec, lies at around Ec
~ 300 kV/cm for the frequency used (10 kHz). Note that Ec is frequency dependent in
any ferroelectric material [31], which increases on increasing frequencies. Still, there is
a little asymmetry likely related to little differences in the metal-insulator interfaces.
199
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.31 – Ferroelectric domain switching current once subtracted the nonferroelectric contributions (left axis) and polarization (right axis) versus applied
electric field of (Bi0.9La0.1)2NiMnO6 thin films.
The hysteresis loops of polarisation versus the applied electric field, P(E), is
computed by determining first the charge related to the ferroelectric domain switching
current (see Sect. 3.3):
QFE = ∫ I FE (t )dt
(5.3)
integrated over the time of the cycle. Then the polarisation is extracted, P = QFE/A,
where A is the area of the round-shaped electrodes (0.25 mm of radius). Note that as Iε
has been substracted in this measurement, the hysteresis loops P(E) should be
rectangular-shaped, i.e. without the positive slope at high electric fields, as corresponds
to all dielectrics, P = ε0(εr -1)E. The results are shown in Fig. 5.31 (right axis). As
observed, the hysteresis loop is quite asymmetric, giving rise to a not closed loop. This
is due to the aforementioned little asymmetry in the IFE(E) curves [Fig. 5.31 (left axis)].
The remanent polarisation is found to be around ~3 μC/cm2. Nonetheless, an exact
value is quite difficult to be determined not only because of this asymmetry, but also
because of the fact that the measured ferroelectric switching current is quite low with
regard to that of the leakage.
200
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.32 – Scheme of the out-of-plane
projection of the polarisation, which is
measured in our experimental set-up.
Still, it is worth remarking that the measured remanent polarisation is a lower bound
for the actual polarisation value since, as discussed in chapter 1, the polarisation axis is
expected to lie along the [111] direction [8] and therefore, according to our
experimental set-up (Sect. 3.1), on applying E from top to top electrode, it is the out-ofplane projection, Pz, of the polarisation vector P what is measured. Given the unit cell
lattice parameters of (Bi0.9La0.1)2NiMnO6 thin films grown on SrTiO3 (determined in
Sect. 5.2) the modulus of P is estimated (see Fig. 5.32) as follows:
P
P = z ;
sin α
where a
tan α =
c 1
⋅
a 2
(5.4)
and c are the in-plane and out-of-plane lattice parameters of
(Bi0.9La0.1)2NiMnO6 thin films. The computed value of the polarisation modulus (~ 5.5
μC/cm2 Eq. 5.4) is still lower than the predicted theoretical value for Bi2NiMnO6: ~18
μC/cm2 or ~28 μC/cm2, depending on the theoretic model that is used for estimating the
polarisation (point-charge model or Berry-phase method, respectively) [32, 33]. Some
reduction in the polarisation of (Bi0.9La0.1)2NiMnO6 films is expected due to the 10% La
doping (note that La is not a stereochemical active ion like Bi). Indeed, this reduction
due to the La-doping may be quite severe, not only because it entails 10% less
ferroelectric polarisable dipoles, but also because this doping may entail the disruption,
at least locally, of the necessary cooperative phenomenon for the ferroelectric order of
the electric dipoles formed by 6s2 lone-pairs of Bi3+. Yet, it is worth noting that the
constraints imposed by the substrate on a thin film were not taken into account in these
predictions, which may significantly modify the polarisation values. Moreover, the large
201
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
discrepancy in polarisation values which both theoretic models give [32, 33] suggests a
rough estimation of the prediction rather than closely exact values.
Finally, for the sake of comparison, it is worth mentioning that the remanent
polarisation of (Bi0.9La0.1)2NiMnO6 thin films, in the order of ~5.5 μC/cm2, is much
smaller than some ferroelectrics of huge polarisation like PbZr0.2Ti0.8O3 (~70 μC/cm2 )
[34] or multiferroic BiFeO3 (~60 μC/cm2) [35] and smaller than conventional
ferroelectrics like BaTiO3 (~20 μC/cm2) [36]. Yet the recorded polarisation is larger
than many multiferroic manganites, such as the rare-earth manganites, which possess
polarisation values of the order of a few nC/cm2 [37].
5.5.3 Ferroelectric phase transition
Once borne out the ferroelectric character of (Bi0.9La0.1)2NiMnO6, and by extension
Bi2NiMnO6, it remains to be deduced the ferroelectric Curie temperature of
(Bi0.9La0.1)2NiMnO6 thin films. Still, due to the increasing large leakage current when
increasing temperature, it greatly hampers measuring the current related to the
ferroelectric domain switching at higher temperatures. Thus, it makes unfeasible to
determine the ferroelectric phase transition temperature by just electric measurements
and therefore the use of indirect techniques becomes necessary. Here, Raman
spectroscopy and temperature-dependent X-ray diffraction measurements were
performed. Single-phase (Bi0.9La0.1)2NiMnO6 thin films, of 70 nm thick, grown at 620ºC
and 0.5 mbar of O2 pressure on SrTiO3 were used.
It is worth remarking that the ferroelectric phase transition of (Bi0.9La0.1)2NiMnO6
thin films might be dramatically different from bulk Bi2NiMnO6 (TFE ~ 485 K [5]), not
only due to the presence of lanthanum, but also because of the fact that the epitaxial
strain exerted by the substrate (SrTiO3) may severely modify the critical temperatures,
as it is the case in most ferroelectric thin films [34, 36, 38 – 41]. We recall here that
(Bi0.9La0.1)2NiMnO6 thin films coherently grown on SrTiO3 are 0.72% tensile strained
(Sect. 5.2.2).
202
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.33 – High frequency phonon mode
associated with stretching of BO6/B’O6
octahedrons and broad low frequency
phonon
mode
associated
stretching
and
BO6/B’O6
octahedrons
La2NiMnO6
and
bending
with
anti-
vibrations
of
of
Bi2NiMnO6,
La2CoMnO6
double-
perovskites [reproduced from Ref. 42].
Raman spectroscopy is a well adapted technique to investigate phase transitions not
only in pure Bi2NiMnO6 [43] but also lanthanide double-perovskites based on Ni – Mn
and Co – Mn cations at the B-site [42 - 44]. Despite being different compounds, they
show similar features in their Raman spectra. Characteristic to these double-perovskite
structures is the presence of a pronounced phonon mode around 600 cm-1 and a broad
phonon mode around 500 cm-1, associated with stretching and antistretching/bending
vibrations of BO6/B’O6 octahedrons, respectively (Fig. 5.33) [42 - 44]. Structural
transitions in these double-perovskites were proved to have an impact in the temperature
dependence of the phonon frequency of these modes, ω(T), shifting its frequency
position around the transition temperature, Δωlattice [42 - 45]. Importantly enough for the
purpose of determining the ferroelectric Curie temperature is the fact that the high
frequency mode, i.e. the one corresponding to the stretching vibrations of MnO6/NiO6
octahedrons, was demonstrated to be very sensitive to these phase transitions [42 - 44],
i.e. maximising Δωlattice.
203
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig.
5.34
–
Temperature
dependence of the Raman spectra
of the high frequency mode of
(Bi0.9La0.1)2NiMnO6 thin films.
The Raman spectra of the high-frequency mode, ω(T), from (Bi0.9La0.1)2NiMnO6
thin films obtained at different temperatures is depicted in Fig. 5.34. As observed, ω(T)
shifts to low wavenumbers as temperature increase, consistent with the temperature
evolution of Raman spectra of Bi2NiMnO6 and lanthanum double-perovskites [42 - 44].
The temperature dependence of ω(T) is plotted in Fig. 5.35 (left axis, solid symbols),
which shows a change of slope around 430 K. Moreover, this signature is more
pronounced in the temperature dependence of the corresponding linewidth,
characterised by the FWHM [Fig. 5.35 (right axis, open symbols)]. These characteristic
changes in ω(T) and FWHM(T) occur at temperatures remarkably close to TFE of bulk
Bi2NiMnO6 (~485 K [5]). Thus, it suggests that the structural transition observed in Fig.
5.35 occurring at around 430 K (with a rough error of ±20 K) should correspond to the
ferroelectric phase transition of (Bi0.9La0.1)2NiMnO6 thin films.
204
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.35 – Temperature dependence of the phonon frequency (solid square symbols,
left axis) and linewidth (open triangular symbols, right axis). The dashed lines indicate
the slope change of the temperature dependence of phonon frequency and linewidth
around TFE.
To bring additional evidence for this transition, X-ray diffraction data (in particular
symmetric θ/2θ diffractograms, see Sect. 2.2.1) were recorded as a function of
temperature (between 200 K and 470 K). We recall here that (Bi0.9La0.1)2NiMnO6 thin
films grow completely strained on SrTiO3 (see Sect. 5.2.2). Therefore, as the film are
in-plane clamped to the substrate all evidence related to structural changes lies in the
out-of-plane lattice parameter, which was obtained from the corresponding angular
position of the (003) Bragg reflexions of the θ/2θ diffractograms at each temperature
(Appendix A).
Fig. 5.36 (left axis) shows the temperature dependence of the out-of-plane lattice
parameter of both (Bi0.9La0.1)2NiMnO6 film and SrTiO3 substrate (corresponding to
cBLNM and cSTO, respectively). Due to thermal expansion, cSTO(T) linearly increases over
the full temperature range with a thermal expansion coefficient, αSTO ~ 4.2 × 10-5 Å/K. In
contrast, cBLNM(T) is non monotonic and clearly displays a kink at about 450 K pointing
to a phase transition occurring at this temperature. A straight line is plotted to emphasis
the fact that the film lattice parameter, below 450 K, gradually deviates from the normal
linear behavior.
205
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.36 – (left axis) Temperature dependence of the out-of-plane lattice parameter of
both substrate (solid square symbol) and (Bi0.9La0.1)2NiMnO6 thin film (solid triangle
symbol);
(right
axis)
Temperature
dependence
of
the
tetragonality
of
(Bi0.9La0.1)2NiMnO6 thin films (star symbols). The dashed line shows the fitting using
Eq. 5.6.
This transition can be even better appreciated in the tetragonality ratio
cBLNM(T)/aBLNM(T), where aBLNM(T) stands for the in-plane lattice parameter of
(Bi0.9La0.1)2NiMnO6 film. In computing this ratio it is assumed that (Bi0.9La0.1)2NiMnO6
film remains coherent on the SrTiO3 substrate and thus aBLNM(T) = aSTO(T), where
aSTO(T) denotes the in-plane lattice parameter of SrTiO3; from the cubic structure of
SrTiO3 it follows that aSTO(T) = cSTO(T) and thus aBLNM(T) = cSTO(T). These tetragonality
values are depicted in Fig. 5.36 (right axis). The enhancement of the (c/a)BLNM(T) is very
apparent at low temperatures and gradually reduced when approaching 450 K. This
behaviour is obviously consistent with having a ferroelectric phase below this
temperature, in which the spontaneous polarization induces an enlargement of the outof-plane lattice parameter [34, 36, 40, 41, 46]. The tetragonality ratio cBLNM(T)/aBLNM(T)
data can be well fitted (dashed line through the data) by using:
0
*
⎧⎪c
BLNM (T ) = cBLNM + α BLNM × T + B × T − T
⎨
0
⎪⎩ aBLNM (T ) = aSTO (T ) = aSTO + α STO × T
206
(5.5)
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
0
where αSTO × T and αBLNM × T terms correspond to the thermal expansion and aSTO
and
0
cBLNM
the extrapolation at 0 K of the lattice parameter of SrTiO3 and
(Bi0.9La0.1)2NiMnO6, respectively. The B × T * − T expansion term of the out-of-plane
lattice parameter, where B and T* are fitting constants, has been proved to be
accomplished in ferroelectric perovskites driven by the stereochemical activity of the
lone-pair of Bi, like BiFeO3, when spontaneous polarisation develops at temperatures
below T* [40]. The excellent fitting of our data to this function, where T* is found to be
450 K, gives an additional hint on the nature of the transition observed at T*, which we,
thus, identify with the ferroelectric transition temperature of (Bi0.9La0.1)2NiMnO6 thin
films.
Therefore, both x-ray diffraction and Raman spectroscopy data indicate that the
ferroelectric phase transition in (Bi0.9La0.1)2NiMnO6 thin films occurs around TFE ~ 450
K (note that Raman technique does not allow determining the critical temperature value
with a good accuracy), which is somewhat reduced compared to bulk Bi2NiMnO6 one
(~ 485 K [5]). This reduction could just be due to the partial replacement of Bi by La;
however, as a matter of fact, in Bi2NiMnO6 films on NdGaO3, a similar TFE has been
reported thus suggesting that strain rather than Bi-La substitution is the dominant effect
on the TFE reduction. However, having said that, it is remarkable that the sensitivity of
these double perovskites on strain is much more modest than typically found in other
ferroelectric, such as BaTiO3, whose Curie temperature is strongly dependent on strain
[36]; indeed, in a 0.70 % of tensile strain, as found here, produces a change of TFE by
about 150 K [36]. Yet it may be enlightening to notice that in BiFeO3 TFE remains also
roughly unchanged for 0.70% of tensile strain [40]. Thus, it seems to be reasonable to
argue that the ferroelectric mechanism might play a role in the strain sensitivity of the
ferroelectric properties. Note that the ferroelectric order in Bi-driven ferroelectric
perovskites, like BiFeO3 and Bi2NiMnO6, is of electronic nature (displacement of the
lone-pair electrons away from the centrosymmetric positon), whereas conventional
ferroelectrics, like BaTiO3, consist of ionic displacements of d0-cations, which are likely
to be, the latter, much more sensitive to lattice distortions.
207
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
5.6 Electric and magnetoelectric
properties
5.6.1 Background
One of the interesting features multiferroic materials may exhibit is the so-called
magnetoelectric coupling (as explained in Sect. 1.1.3), which consists of the coupling
between the ferroelectric and the magnetic order. Due to the poor insulating features of
many multiferroics, an extensive route to investigate the magnetoelectric character
consists of studying the effect on the dielectric permittivity, ε, of changes of the
magnetic state of the magnetic layer, either by applying a magnetic field, the so-called
magnetocapacitance (or magnetodielectric response), ε(H), or by searching for
variations of ε in the temperature dependence, ε(T), in the vicinity of the magnetic
transition temperature (see Sect. 1.1.3).
However, determining the intrinsic dielectric permittivity, and therefore the real
dielectric response of multiferroics, can be, by itself, an arduous task, as explained in
Sect. 3.2.3 and as noticed in BiMnO3 thin films (Sect. 4.4.4). First, as observed in many
dielectrics, extrinsic contributions, such as parasite capacitances formed at the interface
between the dielectric film and the electrodes or at the grain boundaries in ceramic
samples, very often account for the apparent colossal dielectric constants (see Sect.
3.2.3). Second, the leaky behavior of most multiferroic materials may give rise to
apparent large magnetodielectric response, when in reality it might not be the
permittivity but the resistivity of the dielectric material that is changing either on
applying a magnetic field or with temperature (see Sect. 3.2.3 and 3.2.4). Moreover, the
resistivity of (Bi,La)2NiMnO6 is still to be addressed, which is of the highest relevance
in double-perovskites due to the multivalent configuration of the B-cations that may
greatly enhance the conductivity of these materials.
These difficulties become apparent when comparing dielectric data reported for
double-perovskite thin films. It has been reported that La2NiMnO6 films show
temperature (T) dependence and frequency (ν) dependence of the dielectric permittivity
ε(T,ν) [47], which was attributed to temperature-dependent electric dipole relaxation.
208
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Yet the reported ε(T,ν) curves [Fig. 5.37 (a)] resemblances, to a large extent, to the
simulations of a Maxwell-Wagner type of relaxation described in Sect. 3.2.3 (see Fig.
3.10 in Sect. 3.2.3), the behaviour of which was ascribed to the formation of a parasite
capacitance at the interface electrode-dielectric and the temperature dependence of the
resistivity of the dielectric film. On the other hand, the reported ε(T) for Bi2NiMnO6
thin films at 100 kHz [30] shows a modest value (ε ~ 50) at low temperatures whilst an
unexpected sharp increase takes place at 150 K (ε ~ 450) [Fig. 5.37 (b)], which was
claimed to be due to the set of the magnetic order. Still, this ε(T) could again be
reproduced by a Maxwell-Wagner type of relaxation, as shown in our simulations in
Fig. 3.10 (Sect. 3.2.3). Similar ε(T) features were reported for Bi2NiMnO6/La2NiMnO6
multilayers [48]. Instead, a soft monotonous increase of ε along T was reported for
Bi2NiMnO6 thin films at 1MHz [8], where ε varies from 145 to 155 in the range of
temperatures comprised between 20 K to 200 K. Having said that, though, it is worth
mentioning that the dielectric permittivity of bulk Bi2NiMnO6 greatly differs to what is
reported in thin films, as found to be 200 around room temperature, with the sharp
increase around 485 K corresponding to the ferroelectric transition temperature [5].
Fig. 5.37 – (a) Frequency dependence of the dielectric permittivity of La2NiMnO6 thin
films at different temperatures reproduced from Ref. 47; (b) Temperature dependence
of the dielectric permittivity (right axis) and magnetocapacitance (left axis) of
Bi2NiMnO6 thin films reproduced from Ref. 30.
Regarding the magnetoelectric coupling, Bi2NiMnO6 thin films were reported to
exhibit ~1% magnetocapacitance [(C(H)-C(0))/C(0)] [30]. Yet, as demonstrated in sect.
209
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
3.2.4, this magnetocapacitance effect may easily arise from magnetoresistance effect,
which was neither elucidated in that report.
The lack of a thorough frequency and temperature dependent dielectric study in the
literature, together with the absent deconvolution between contributions of the resistive
part and the dielectric part, inhibits from discerning whether the reported dielectric and
magnetoelectric properties of (Bi,La)2NiMnO6 thin films were intrinsic or extrinsic,
thus claiming for a new regard on data and conclusions. Here in this section we
performed an exhaustive study of the dielectric properties of (Bi0.9La0.1)2NiMnO6 thin
films, in which temperature dependent impedance spectroscopy (see Sect. 3.2) was used
to disentangle extrinsic and intrinsic contributions to the measured permittivity. At the
end of the section, the intrinsic magnetoelectric response of (Bi0.9La0.1)2NiMnO6 thin
films is obtained by deconvoluting magnetodielectric and magnetoresistive effect. To
performed the dielectric measurements, Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 capacitors
were fabricated (see Sect. 3.1). (Bi0.9La0.1)2NiMnO6 samples were grown at the
optimised conditions for single-phase formation (i.e. at 620 ºC and 0.5 mbar of O2
pressure). The thickness of the set of samples was comprised between 100 and 110 nm.
5.6.2 Complex dielectric constant and ac
conductivity. Qualitative analysis
Fig. 5.38 depicts the temperature dependence of the dielectric permittivity at
different frequencies, assuming that the measured capacitance is only due to the
dielectric response of (Bi0.9La0.1)2NiMnO6 film, i.e. C = ε’ε0A/(2t) (see chapter 3). The
dielectric permittivity ε’ increases as temperature rises, with a well visible step-like
behaviour. The step-like feature moves toward higher temperatures on increasing
frequency, similar to what was reported for La2NiMnO6 thin films [47]. Moreover, the
reported dielectric permittivity of Bi2NiMnO6 thin films measured at 100 kHz and at 1
MHz of Ref. 30 and Ref. 8 shows a clear resemblance to our data in Fig. 5.38 for 100
kHz and 1 MHz, respectively. Nonetheless, the fact that ε’ at high temperatures is
clearly frequency-dependent and it strongly reduces when frequency is increased,
suggests that extrinsic effects are contributing to the dielectric response (see chapter 3).
210
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig.
5.38
–
Temperature
dependence
of
the
dielectric
permittivity
of
Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 system measured at different frequencies.
In order to assess the frequency response, the complex representation of the
dielectric constant, ε* = ε’ – iε”, will be used (see Sect. 3.2.2). Fig. 5.39 (a) and (b)
depict the frequency dependence of the effective capacitance [C = ε’ε0A/(2t)] and the
loss tangent (tanδ = ε”/ε’), respectively, of Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 capacitors
at different temperatures. The measured capacitance [Fig. 5.39 (a)] shows the existence
of two frequency regimes, where the C(ν) [and thus the permittivity ε’(ν)] is rather
constant, separated by a step-like region which is accompanied by a peak of tanδ(ν) and
thus the imaginary part of the dielectric constant, ε” [Fig. 5.39 (b)]. Both the step-like in
ε’(ν) ∼ C(ν) and the peak of tanδ(ν) shift toward higher frequencies on increasing
temperature. At first sight, this behaviour could be attributed to thermally activated
Debye-like dielectric relaxation dominating the frequency dependence of ε’(ν) [49],
with a thermal activation energy of Ea ~ 75 meV for temperatures higher than 100 K
(Fig. 5.40) following:
⎡E ⎤
τ= 1
= τ 0 exp ⎢ a ⎥
ωmax
⎣ k BT ⎦
(5.6)
where ωmax is the angular frequency (2πν) at which the peak of ε” appears and kB is the
Botzman constant (Sect. 3.2). Nonetheless, it is demonstrated in chapter 3 that a
211
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Maxwell-Wagner relaxation type may produce identical effects. The low-frequency
dielectric permittivity, obtained assuming that the dielectric response is due to a unique
capacitance, ε’ = C·(2t/ε0A), is anomalous high (ε’ ~ 1000) as shown in Fig. 5.39. In
contrast, at higher frequency the capacitance is about one order of magnitude smaller, ε’
~ 100, which is indeed found to be in the range of that reported for Bi2NiMnO6 bulk
materials, thus signalling a more plausible intrinsic character.
Fig. 5.39 – Frequency dependence of the effective capacitance (a) and the loss tangent
(b) of Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 capacitors measured at different temperatures.
The dashed line signals the frequency at which magnetocapacitance measurements
were performed (see Sect. 5.6.4)
212
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.40 – Time constant, τ, in natural logarithm scale as a function of the inverse of
temperature (correlated to the temperature in the upper scale).
In the high frequency range, one can also observe [Fig. 5.39 (a)] a small but
perceptible ε’(ν) dependence, which is at odds with the response of an ideal dielectric,
but commonly observed in most of them and attributed to the non-ideality of the
dielectric response, associated with the frequency dependent ac-conductivity σac (see
Sect. 3.2). This can be better seen in Fig. 5.41 where we plot the frequency dependence
of the real part (σ’) of the complex conductivity (σ* = iωε0ε*) at various illustrative
temperatures (80 K, 110 K and 140 K). σ’ should be the sum of the frequencyindependent dc-conductivity (σdc), which is always present due to the leakage of the
dielectric, and a frequency-dependent term σac, that typically shows a power-law
dependence on frequency σac = σ0ωα, α ≤ 1 [49 – 51] (see Sect. 3.2.2). The σ’(ν) log-log
data in Fig. 5.41 indeed shows that at high frequency there is a power-like σac(ν)
contribution superimposed to σdc term responsible for the flattening of σ’(ν) at
intermediate frequencies. The extrapolation of σ’(ν) from the plateau towards zero
frequency (dashed lines in Fig. 5.41) allows to estimate the σdc of the material or,
equivalently, the resistivity at any temperature. Some illustrative values are shown in
the inset of Fig. 5.41 (solid square symbols) where a rough exponential increase of
resistance when lowering temperature can be appreciated. When further lowering ν,
213
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
conductivity is steeply reduced, deviating for the ideal behaviour marked in dashed
lines. As shown by data in Fig. 5.41, this drop is also temperature dependent, and shifts
toward higher frequencies as temperature rises. Not surprisingly, it coincides with the
large enhancement of the dielectric constant shown in Fig. 5.39 (a) and the peak of ε”
[Fig 5.39 (b)].
Fig. 5.41 – Frequency dependence of σ’ at different temperatures. The dashed line
indicates the ideal behaviour, σ’ = σ’dc + σ’0ωα (see text). The inset shows the
temperature dependence of the resistivity obtained by extrapolation to zero frequency of
σ’ from the main panel (solid squares) and by impedance spectroscopy (open squares),
the latter exposed in Sect. 5.6.3. Solid lines are visual guides.
In the following it will be shown that both, the low-frequency region as well as the
step-like region are not-intrinsic properties of (Bi0.9La0.1)2NiMnO6 film but result from
the contribution of interface effects.
5.6.3 Impedance spectroscopy. Quantitative
analysis
To obtain a more quantitative insight into the dielectric response of the sample, to
investigate the number of electrical responses present and to determine the intrinsic
214
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
properties of the film, complex impedance (Z* = Z’ + iZ”) spectroscopy was performed
as described in Sect. 3.2.1.
Fig. 5.42 – (a) Impedance complex plane (–Z’’ – Z’ plots) from impedance data
measured at 110 K. The visual guide of the dashed line indicates the two semicircles at
high and low frequency. The inset sketch depicts the equivalent circuit, describing the
different electrical responses present in Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 capacitors
(see text for symbols). (b) –Z’’ – Z’ data plots measured at different temperatures.
In Fig. 5.42 (a) illustrative –Z” - Z’ plot of the impedance measured at 110 K is
shown. Data signals the existence of two incomplete semicircles (marked with dashed
lines as guide-to-eyes) at high and low frequency, respectively. The existence of these
semicircles indicates that there are two electrical contributions to the frequency
dependent impedance. Thus, as suspected, the dielectric response observed in Sect.
5.6.2 does not only come from the intrinsic dielectric properties of (Bi0.9La0.1)2NiMnO6
film, which would produce a unique semicircle (Sect. 3.2.1). This behaviour is hence
quite consistent with a Maxwell-Wagner relaxation, as explained in Sect. 3.2.3. On the
other hand, it can be appreciated in Fig. 5.42 (a) that the radius of the low-frequency
semicircle is much larger than the high-frequency one; this reflects that the lowfrequency contribution is much more resistive than that of the high-frequency
contribution. Additionally, inspection of the impedance data at different temperatures,
shown in Fig. 5.42 (b), indicates that the high frequency semicircle significantly
215
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
decreases on increasing temperature, evidencing that the resistivity of the high
frequency contribution decreases as temperature rises, according to data of the
conductivity shown in Fig. 5.41.
Fig. 5.43 – Sketch of the dielectric behaviour of (Bi0.9La0.1)2NiMnO6 thin films when the
resistivity of the film and interface parasitic capacitance interferes.
Thus, according to Fig. 5.42, the most natural explanation of the dielectric
behaviour shown in section 5.6.2 comes from the formation of a capacitive layer at the
interface and by the temperature dependence of the resistivity of the core of the film, as
deduced in Sect. 3.2.3. The band bending caused by the difference between the work
function of the metal and the electronic affinity of the dielectric gives rise to charge
depletion/accumulation region at the interface [50, 52 – 54], which forms a relatively
thin layer, behaving as a high resistive barrier, modelled as a capacitor, Cext, and a low
conductance, Rext-1, connected in parallel as illustrated by the circuit-model sketched in
Fig. 5.42 (a). At high frequency, charge carriers have no time to follow the alternating
electric field and the measured capacitance is the film and the interface capacitances in
series (Fig. 5.43). However, at low frequencies, charge carriers do respond to the
216
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
electric field in the low resistive part, i.e. the core of the film [modelled as R inset Fig.
5.42 (a)], forming an electric current. This entails that the drop of the electric field is
mostly taking place at the interface barrier, yielding the apparent high dielectric
constant shown in Fig. 5.39 (a) because of the apparent reduction of the dielectric
thickness (measured capacitance ~ 1/t’) as shown in Fig. 5.43 [52]. On increasing
temperature, the film resistivity decreases [so leakage, σdc, increases (Fig. 5.41)] and
charge carriers can respond to faster alternation of the electric field. Thus, the apparent
enhancement of the dielectric constant due to the apparent reduction of the dielectric
thickness is shifting toward higher frequencies on increasing temperature, consistent
with the observed temperature evolution of data of Fig. 5.39 (a). The cut-off frequency,
ωmax, at which losses (∼ε’’) show a peak [Fig. 5. 39 (b)] is given by the condition
ωmax(T) = [R(T)·C]-1 [52] and is therefore temperature dependent. Hence, it is more
reasonable to argue that the thermal activation of this apparent dielectric relaxation is
driven by the temperature-dependence of the resistivity, instead of permanent dielectric
dipoles suggested for La2NiMnO6 films [47]. Indeed, the dielectric relaxation of
permanent dipole moments tends to occur at much higher frequencies, in the range of
the microwaves [55], as indicated in Sect. 3.2.2.
Consequently, the impedance of Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 system (film +
extrinsic contribution) is given by adapting of Eq. 3.10 in Sect. 3.2.3:
Z * ( R − CPE , Rext − Cext ) =
Rext
R
+
α
1 + iω ⋅ Rext ⋅ C ext
1 + R ⋅ Q ⋅ (iω )
(5.7)
where the first and the second terms correspond to the film and the extrinsic
contributions, respectively. A CPE element (see Sect. 3.2.1) is used for the film
contribution accounting for the non-ideality of the dielectric behaviour shown in Sect.
5.6.2. Eq. 5.7 was used to fit impedance data in order to validate the proposed model.
Fig. 5.44 shows some illustrative results of the fits to -Z’’– Z’ data at different
temperatures. As observed, model (solid lines) and data match very reasonably, which is
also extensive for the rest of temperatures up to 170 K. Above this temperature the lowfrequency contribution dominates almost completely the experimentally available
217
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
frequency range (up to 1 MHz), and accurate extraction of the intrinsic properties (highfrequency contribution) was unfeasible.
Fig. 5.44 – Experimental data (open symbols) and fitting (solid line) using the model of
Eq. 5.7 for some illustrative temperatures. The inset zooms the high-frequency region.
Fig.
5.45
dependence
exponent.
218
–
of
Temperature
the
CPE
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Importantly enough, the fitting allows disentangling intrinsic and extrinsic
contribution in the impedance data. The fitting values of the R-CPE element (R, Q, α),
corresponding to the film contribution, are summarised in table 5.5. It is worth noticing
that the CPE exponent, α, which decreases on increasing temperature (Fig. 5.45),
pointing to an enhanced non-ideality of the dielectric behaviour of (Bi0.9La0.1)2NiMnO6
films upon heating, displays a defined anomaly at about 100 K, closely coinciding with
the ferromagnetic Curie temperature. From the R, Q and α values the intrinsic dielectric
permittivity [ε = C·(2t/ε0A), where C = (Q·R)(1/α)/R, see Appendix C] and resistivity [ρ =
A·R/(2t)] of (Bi0.9La0.1)2NiMnO6 films can be computed at each temperature, as shown
in Fig. 5.46 and 5.47, respectively. For the sake of clarity, in the following dielectric
permittivity and resistivity are exclusively referring to the intrinsic properties of
(Bi0.9La0.1)2NiMnO6 films, obtained as aforementioned by impedance spectroscopy.
Temperature
(K)
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
Q [Fsα-1]
3.07·10-9
3.46·10-9
3.43·10-9
3.52·10-9
3.72·10-9
3.81·10-9
4.04·10-9
4.31·10-9
4.85·10-9
5.77·10-9
7.11·10-9
7.51·10-9
7.89·10-9
1.01·10-8
1.21·10-8
1.67·10-8
2.56·10-8
error Q
[%]
5.0
4.5
4.7
4.4
4.1
4.0
3.5
3.2
3.2
3.2
3.5
4.1
4.5
5.1
5.4
6.5
11.6
R [Ω]
3.19·105
1.61·105
1.70·105
1.41·105
9.93·105
8.99·105
5.97·105
4.35·105
3.12·104
2.13·104
1.13·104
6.98·104
5.30·103
2.58·103
2.04·103
1.15·103
6.00·102
error R
[%]
9.1
5.7
6.1
5.3
4.3
4.0
3.2
2.5
2.2
1.8
1.6
1.5
1.4
1.3
1.3
1.4
1.7
α
0.926
0.921
0.922
0.920
0.918
0.916
0.913
0.908
0.900
0.888
0.875
0.874
0.872
0.859
0.849
0.832
0.809
error α
[%]
1.2
0.8
0.9
0.8
0.6
0.6
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.5
0.7
Table 5.5 – Fitting results of the high-frequency R-CPE element, sketched in Fig. 5.43
(a).
The dielectric permittivity of (Bi0.9La0.1)2NiMnO6 films (Fig. 5.46) is found to be
temperature independent, as expected for a ferroelectric material far below its
ferroelectric transition temperature [~450 K (Sect. 5.5.3)]. It is rewarding to notice that
219
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
the value of permittivity (∼ 220) is in close agreement with the reported bulk value
(~200) [5]. It is also worth noting that around the magnetic ordering temperature TFM
(~100 K) there is no significant deviation of permittivity; however, its derivative dε/dT
shown in Fig. 5.46 (right axis), seems to indicate a subtle variation at a temperature
close to the magnetic transition temperature, much as the anomaly at 100 K of the
exponent α (Fig. 5.45), suggesting a possible small influence of the magnetic order and
thus magnetoelectric response.
Fig. 5.46 – Temperature dependence of the intrinsic dielectric permittivity of
(Bi0.9La0.1)2NiMnO6 films (left axis) and dielectric permittivity derivative (right axis).
The temperature dependence of the resistivity, ρ(T), (Fig. 5.47) shows a
semiconductor-like behaviour, similar to what has been reported for other multiferroic
perovskite oxides [53]. The resistivity decreases from ~108 Ω·cm at 20 K to ~104 Ω·cm
at 170 K. The resistivity values obtained by impedance spectroscopy and σdc or,
equivalently, the resistivity estimated by extrapolation of σ’(ν) from the plateau towards
zero frequency (dashed lines in Fig. 5.41) are, as expected, in good agreement, as shown
by some illustrative values in Fig. 5.41 (inset). At temperatures above 100 K, the
resistivity seems to behave thermally activated, following an Arrhenius law, ρ =
ρ0exp(Ea/kBT), (dashed line in Fig. 5.47) with an activation energy (71 ± 5 meV). This
value is remarkable close to the one obtained from Eq. 5.6, bearing out the claim stated
220
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
before that the thermal activation of the apparent dielectric relaxation observed in Sect.
5.6.2 is driven by the temperature dependence of the resistivity of (Bi0.9La0.1)2NiMnO6
film.
Fig. 5.47 – Temperature dependence of the intrinsic resistivity of (Bi0.9La0.1)2NiMnO6
films. The dashed line shows the Arrhenius fitting.
Dashed region indicates the
magnetic Curie temperature.
Within the simplest picture, electron transport in (Bi0.9La0.1)2NiMnO6 is related to
electron hopping among dissimilar electronic configuration of the B-cations, i.e. Ni2+
and Mn4+, which would entail a valence band formed by Ni2+ eg spin up and the
conduction band formed by Mn4+ eg spin up (Fig. 5.48). The low activation energy
found suggests that (Bi0.9La0.1)2NiMnO6 films possess a small band gap, behaving more
similar to a semiconductor material. Instead, for BiMnO3 thin films (Sect. 4.4), a larger
activation energy is found (Ea ~ 200 meV). Therefore, it might be possible that
multiferroic double-perovskite materials may suffer from a poorer insulating character
with regard to their counterpart single-perovskites, favoured by the dissimilar electronic
configuration of the B-cations and their B-site order, which shrinks the gap. Not
surprisingly, small activation energy was also reported for B-site ordered doubleperovskite La2NiMnO6 thin films (Ea ~ 32 meV) [47]. However, it is worth mentioning
221
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
that the observed activation energy is noticeble much smaller than the predicted band
gap in Bi2NiMnO6 (~200- 500 meV) [32, 33].
Fig. 5.48 – Sketch of the band diagrams of Ni2+ and Mn4+ in Bi2NiMnO6, adapted from
the density of states predicted for Bi2NiMnO6 in Ref. [5].
A different behaviour is found, though, at lower temperature (T < 100 K). As shown
in Fig. 5.47, in this temperature range the resistivity deviates from the Arrhenius law,
reflecting a change in the predominant conduction mechanism. Alternative conduction
mechanism, such Mott’s Variable-Range-Hopping (VRH) or Efros and Shklovskii VRH
conduction mechanisms [ρ = ρ0exp(T0/T1/γ), γ = 4 or 2, respectively] have been
considered [56 - 60], as shown in Fig. 5.49. It is found that none of these models allow
describing satisfactorily the whole temperature range, either. Moreover, VRH model, in
which electron hopping is not produced between first neighbour ions but there is an
optimum hopping distance that maximise the hopping probability [60], is proposed for
either disordered systems or with doping impurities, in which localised states are found.
As this case is not expected in (Bi,La)2NiMnO6 films, the conduction mechanism shown
in Fig. 5.47 has more physical meaning. In any event, data in Fig. 5.47 suggests either a
change of the transport mechanism or the relevant energy for activated transport
occurring at about 100 K. Interesting enough, at this temperature the film becomes
222
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
ferromagnetic. Thus, it might be quite plausible that the magnetic order may have some
influence in the conduction mechanism, especially if the electron transport is expected
to be driven by electron hopping between the d-orbitals of the magnetic ions, Ni2+ and
Mn4+.
Fig. 5.49 – Resistivity as a function of (1/Tempereture)1/γ, being γ =2 (a) and γ = 4 (b).
The dashed region indicates the ferromagnetic Curie temperature.
5.6.4 Magnetoelectric response
In order to detect any magnetoelectric effect in the dielectric properties of
(Bi0.9La0.1)2NiMnO6 films, dielectric measurements were performed under the presence
of a magnetic field and without. The magnetic dependence of the effective capacitance,
C(H), of Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 system, assuming that the measured
capacitance is only due to the dielectric response of (Bi0.9La0.1)2NiMnO6 film as
exposed in Sect. 5.6.2, C = ε’ε0A/(2t), was obtained at 100 kHz for different
temperatures. The magnetocapacitance, defined as MC = [C(H)-C(0)]/C(0) as described
in Sect. 3.2.4, is shown in Fig. 5.50 (a) for several temperatures. The MC curves are
very much similar to the magnetocapacitance reported for Bi2NiMnO6 thin films [30]. It
turns out that, at a given magnetic field, the temperature dependence of the
magnetocapacitance, MC(T), displays a non-monotonic dependence on temperature, as
shown in Fig. 5.50 (b), attaining a maximum (4.5 % at 8 T) around 140 K. Data shows a
clear resemblance to the MC(T) reported for Bi2NiMnO6 films [30], shown in Fig. 5.37
(b) (left axis).
223
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
Fig. 5.50 – (a) Magnetocapacitance of Pt/(Bi0.9La0.1)2NiMnO6/Nb:STO system
measured at 100 kHz at different temperatures. (b) Temperature dependence of the
magnetocapacitance of Pt/(Bi0.9La0.1)2NiMnO6/Nb:SrTiO3 system at H = 8 T and 100
kHz. Dashed line are guide-to-eyes.
Nonetheless, the maximum of the magnetocapacitance effect occurs at a
temperature substantially above the ferromagnetic transition temperature (~100 K)
where the largest magnetoelectric response due to the coupling between the ferroelectric
and magnetic order is to be expected [61]. Moreover, at 100 kHz, the ε’(ν) and tanδ(ν)
data in Fig. 5.39 indicate that the temperature range in which MC(T) shows the sharp
increase coincides with the step-region in ε’(ν = 100 kHz) [marked with dashed line,
Fig. 5.39 (a)] separating the two frequency regimes: the extrinsic low-frequency and the
intrinsic high-frequency dielectric constant regimes. Indeed, at 100 kHz, for
temperatures in which ε’ is found either on the low-frequency plateau or the high224
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
frequency plateau [Fig. 5.39 (a), marked with the dashed line], MC(H) is almost
inexistent (Fig. 5.50). This suggests that the observed large MC effect may occur due to
the shift of the step-like dielectric response because of the magnetic-field inducing
change in film resistivity. As demonstrated in Sect. 3.2.4, a Maxwell-type of relaxation,
in which the film resistivity changes on applying a magnetic field, ρ(H), would produce
identical effects, without having a magnetoelectric coupling between the ferroelectric
and magnetic order. In particular, if ρ(H) decreases on increasing H, a positive MC peak
is expected, as shown in the simulation of Fig. 3.13 (Sect. 3.2.4), reproducing data of
Fig. 5.50 (b). As a matter of fact, ρ(T) curve of (Bi0.9La0.1)2NiMnO6 film shown in Fig.
5.47 show clear indications of the magnetic order having some influence.
Hence, as exposed in Sect. 5.6.3, magneto-impedance spectroscopy was performed
in order to disentangle extrinsic and intrinsic effects, in particular, in order to
deconvolue magnetoresistive effects from that coming from the genuine coupling of the
two ferroic orders. Two set of impedance data were collected following the same
procedure described in Sect. 5.6.3, one without applying a magnetic field and one with
the presence of a magnetic field (H = 0 T and H = 9 T), in a temperature range close to
the ferromagnetic transition temperature (80 K – 130 K). In both cases, as expected, two
incomplete semicircles were observed in the –Z’’-Z’ plots as shown in Fig. 5.42 (a), and
with the same temperature dependence as shown in Fig. 5.42 (b). Fitting both set of data
with Eq. 5.7, i.e. using the same impedance circuit model of Sect. 5.6.3, the fitting
values R, Q and α of the R-CPE element related to the intrinsic impedance response of
(Bi0.9La0.1)2NiMnO6 film can be obtained for each temperature, with and without an
applied magnetic field. From these values it is computed the intrinsic dielectric
permittivity, ε(T, H), and resistivity, ρ(T, H), of (Bi0.9La0.1)2NiMnO6 film, as described
in Sect. 5.6.3. In the following, for the sake of simplicity, dielectric permittivity and
resistivity will exclusively refer to the intrinsic dielectric and resistive properties of
(Bi0.9La0.1)2NiMnO6 film.
Fig. 5.51 (a) shows the temperature dependence of the dielectric permittivity with
and without an applied magnetic field, ε(T, H = 0 T ) and ε(T, H = 9 T ). Despite the
large applied magnetic field, no significant change is observed within the experimental
error. On the contrary, when plotting in Fig. 5.51 (b) the magnetoresistance of
(Bi0.9La0.1)2NiMnO6 film, i.e. MR = [ρ(T, H = 9 T) – ρ(T, H = 0 T)]/ρ(T, H = 0 T), the
225
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
resistivity is found to decrease noticeably when applying a large magnetic field. This
fact provides support to the claim above mentioned that the magnetocapacitance shown
in Fig. 5.50 arise from the magnetoresistive character of (Bi0.9La0.1)2NiMnO6 film
instead of a genuine coupling of the two ferroic orders. Hence, it is reasonable to extend
this conclusion for the reported magnetocapacitance in (Bi,La)2NiMnO6 compounds.
Taking into account that the coupling between the ferroelectric and ferromagnetic order
would entail a change in the dielectric permittivity following Δε ~ αMEM2 (Sect. 1.1.3),
the negligible ε(H) perturbation points out to a weak coupling, if any, between the two
ferroic orders, the causes of which are very likely related to the different mechanisms of
the two ferroic orders (see Sect. 1.2) and their different energy scales (TFM ~ 100 K,
whereas TFE ~ 450 K) in (Bi,La)2NiMnO6 compounds.
Fig. 5.51 – (a) Temperature dependence of the intrinsic dielectric permittivity of
(Bi0.9La0.1)2NiMnO6 films obtained by magneto-impedance spectroscopy for H = 0 T
(open symbols) and H = 9 T (solid symbols). (b) Magnetoresistance of
(Bi0.9La0.1)2NiMnO6 films obtained by magneto-impedance spectroscopy (for H = 0 T
and H = 9 T).
226
Chapter 5. (Bi0.9La0.1)2NiMnO6 thin films
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230
Appendix A: Lattice parameters
from XRD data
A.1 Symmetric XRD scans
As described in Chapter 2, symmetric XRD scans allow the crystallographic planes
that are parallel to the surface of the film to diffract (see Fig. 2.5, Ch. 2). From the
Bragg’s law (Eq. 2.1, Ch. 2), the interplanar distance of the (hkl) planes, dhkl, planes can
be computed from the 2θhkl angle in which diffraction takes place. When (00l)
crystallographic planes are the ones parallel to the surface, the out-of-plane lattice
parameter, c, can trivially be related to the interplanar distance, d00l, following Eq. 2.1:
d 00l =
c
=
l
λ
⎛ 2θ ⎞
2sin ⎜ 00 l ⎟
⎝ 2 ⎠
(A.1)
where λ is the wavelength of the incoming X-ray radiation. Note that this is valid for
orthogonal crystal structures, i.e. cubic, tetragonal and orthorhombic (a complete
description of dhkl of the different crystal structures is found in table A.1). Thus, by
determining 2θ00l position of the (00l) XRD reflexion of the film, the out-of-plane lattice
parameter of the film should be computed. Improvement of the accuracy can be
achieved by Nelson-Riley extrapolation method [1], in which as many as possible of the
(00l) XRD peaks, i.e. different l, is used.
Nonetheless, the diffractometer is not perfect aligned, which entails that the
measured 2θ00l position is shifted from the correct position that should correspond to the
diffraction (00l) planes. An easy way, and used in this work, to correct this shift and
allow accurately estimating the lattice parameters consists of using the substrate lattice
parameter, a, as a reference (considered a virtual perfect crystal), i.e. aSTO = 3.905 Å for
SrTiO3. From the 2θ00l positions of the XRD reflexions of the substrate, 2θs,00l, and
considering aSTO = 3.905 Å, an effective wavelength, λeff, which contains the
instrumental misalignment, can be defined as follows from Eq. A.1:
231
λeff =
aSTO
⎛ 2θ
⎞
⋅ 2sin ⎜ s,00 l ⎟
l
⎝ 2 ⎠
(A.2)
From λeff the out-of-plane lattice parameter of the film is computed as follows:
c film =
l ⋅ λeff
⎛ 2θ
⎞
2sin ⎜ f ,00l ⎟
⎝ 2 ⎠
(A.3)
where 2θf,00l is the measured 2θ position of the film (00l) XRD reflexion.
A.2 Reciprocal space maps
Similar to the lattice parameters extracted from the symmetric XRD scans, the
substrate will be used to account for the instrumental misalignment. Given a (hkl) XRD
reflexion of both substrate and film in the reciprocal space map (RSM), see Sect. 2.2.1,
the film lattice parameters is evaluated by determining Δqhkl ≡ q f , hkl − qs , hkl , where
subscript f and s stand for film and substrate XRD reflexion, respectively. The qs , hkl
position of the substrate (SrTiO3), i.e. (qs,parallel, qs,perp) in the RSM, is used as a
reference with lattice parameter aSTO = 3.905 Å.
In the following, a tetragonal structure is considered for the sake of simplicity (and
due to the fact that it is actually the structure found in the films of this work), yet it is
extensive for the rest of crystal structures, though with more complex expressions (table
A.1). Thus, the out-of-plane lattice parameter of the film, cf, is obtained from Δqperp
with regard to the qperp component of the substrate, as follows:
Δq perp ≡ q f , perp − qs , perp =
lf
cf
−
ls
aSTO
⇒
cf =
lf
ls
aSTO
+ Δq perp
(A.4)
where lf and ls are the l Miller index of the (hkl) reflexion of the film and substrate,
respectively. Similarly, the in-plane lattice parameter of the film, af, is assessed
following:
232
Δq parallel ≡ q f , parallel − qs , parallel =
⇒
af =
h 2f + k 2f
af
hs2 + ks2
−
aSTO
⇒
h 2f + k 2f
(A.5)
hs2 + ks2
+ Δq parallel
aSTO
where hf, kf and hs, ks are the h, k index of the (hkl) XRD reflexion of the film and
substrate, respectively.
The general algebraic expressions of qhkl for the different crystal systems is shown in
the following table, in which a, b, c, α, β and γ are the lattice parameters and the
corresponding angles of the different unit cells (in the conventional notation [2]).
2
1
qhkl = 2
d hkl
Crystal System
(h 2 + k 2 + l 2 )
a2
(h 2 + k 2 ) l 2
+ 2
a2
c
2
2
h
k
l2
+
+
a2 b2 c2
Cubic
Tetragonal
Orthorhombic
Hexagonal
Trigonal
Monoclinic
4
l2
2
2
⋅ (h + k + hk ) + 2
3a 2
c
2
2
2
2
1 ⎛ (h + k + l ) ⋅ sin α + 2 ⋅ (hk + hl + kl ) ⋅ (cos2 α − cos α ) ⎞
⎟⎟
⋅⎜
a 2 ⎜⎝
1 + 2 cos3 α − 3 cos 2 α
⎠
2
2
2
h
k
l
2hk cos β
+ 2 + 2 2 −
2
2
a sin β b
c sin β ac sin 2 β
(1 − cos
Triclinic
2
α − cos 2 β − cos 2 γ + 2 cos α cos β cos γ ) ⋅
−1
h
k2
l2
2kl
2
2
sin
α
+
sin
β
+
sin 2 γ +
(cos β cos γ − cos α ) +
2
2
2
a
b
c
bc
2lh
2hk
+
(cos γ cos α − cos β ) +
(cos α cos β − cos γ ))
ca
ab
⋅(
Table A.1 – Distance between the crystallographic (hkl) planes for the different crystal
structures.
233
References
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Zanotti, M. Catti, Fundamentals of Crystallography, Oxford University Press Inc., New
York, 2002.
234
Appendix B: Diamagnetism of
SrTiO3 substrates
The diamagnetic contribution of SrTiO3 substrates (provided by commercial
company Crystec GmbH), used here for the growth of either BiMnO3 or
(Bi,La)2NiMnO6, was thoroughly studied in previous work in the group in the frame of
the PhD thesis of Dr. X. Martí [1], onto which YMnO3 thin films were grown using the
same PLD facilities (Sect. 2.1). What is reproduced in this appendix is the procedures
previously used [1] to determine the diamagnetic susceptibility of SrTiO3 substrates,
χSTO, the value of which is the one used in this work.
First, in the aforementioned previous work [1], the magnetic field dependence of the
magnetisation, M(H), of a set of as-received bare SrTiO3 susbtrates was measured at 35
K and 300 K. As M = χSTO·H, the negative slope of M(H) curves on increasing H allows
obtaining the volume diamagnetic susceptibility of SrTiO3, χvSTO, at both temperatures,
which were remarkably close: -1.13·10-6 emu/[Oe·cm3] and -1.22·10-6 emu/[Oe·cm3] at
35 K and 300 K, respectively. Note that the volume susceptibility was computed using
the dimensions of SrTiO3 substrates: 5 x 5 x 0.5 mm3.
Second, the diamagnetic susceptibility of SrTiO3 substrates can also be determined
by measuring M(H) curves of different thick films already grown on SrTiO3 substrates
at temperatures belonging to the paramagnetic regime of the film. The M(H) curves
follows M = (χvSTO + χvfilm)·H. The diamagnetic susceptibility will be independent of the
film thickness, as all the substrates are identical in dimensions, but the paramagnetic
susceptibility of the film will be proportional to the film thickness, i.e. χvfilm = K·t,
where K and t are a constant and the film thickness, respectively. Thus, by
differentiating M(H) a linear dependence is found as a function of thickness: dM/dH =
χvSTO + K·t. The interception at t = 0 of the linear fitting allows extracting the volume
diamagnetic susceptibility of SrTiO3, χvSTO = (-1.11 ± 0.05)·10-6 emu/[Oe·cm3], in close
agreement with the one extracted from bare SrTiO3 substrates. This latter value was
used in this work to subtract the diamagnetic contribution of the substrate in the raw
magnetic data.
235
References
[1] X. Martí, Growth and characterization of magnetoelectric YMnO3 epitaxial thin
films,
PhD
thesis,
Universitat
Autònoma
de
Barcelona,
2009.
http://usuaris.tinet.cat/xmarti/talks/xmarti_phd.pdf
236
Appendix C: Capacitance values
from the R-CPE element
As stated in chapter 3, the non-idealty of the dielectric behaviour is usually
accounted by replacing the ideal capacitor, C, by a Constant Phase Element, CPE. Real
dielectrics also display leakage, so that the simplest impedance representation of a non
ideal real dielectric is by an R-CPE element (see Sect. 3.2.1), whose impedance
response is given by the following expression:
Z R* −CPE =
R
1 + RQ(i ⋅ ω )α
(C.1)
where Q and α (α ≤ 1, being α = 1 the ideal dielectric behaviour) denote the amplitude
and the phase of the CPE, respectively. Note that when α = 1, the impedance of the
ideal RC element is obtained (see Eq. 3.2, Sect. 3.2.1) and, thus, Q can be identified as
C. Yet, when α ≠ 1, Q does not have the dimension of capacitance, i.e. [F], but its units
are given by [F· s(α-1)], so it turns out necessary to obtain the real capacitance values of
the R-CPE element in order to correctly assess the dielectric properties.
Fig. C.1 – Simulated –Z’’-Z’ plots (a) and –Z’’ vs frequency curves (b) for a R-CPE
element using different values of CPE exponent, α. α = 1 denotes the ideal RC element.
R and C values taken in the simulation were 1.5·103 Ω and 10-7 F, respectively.
237
The ideal dielectric, modelled by a RC element, shows a semicircle in the –Z”- Z’
plots [Fig. C.1 (a)], the maximum is found for the angular frequency ωmax = (R·C)-1,
which coincides with the peak in the imaginary part of the impedance, Z”, [Fig. C.1
(b)]. This frequency has a physical meaning and corresponds to the cut-off frequency at
which higher frequencies the dielectric character prevails, whereas lower frequencies it
is the leakage character that is predominant (See Sect. 3.2.1). The non-ideality,
modelled by an R-CPE element, shows a depressed semicircle in the –Z’’-Z’ plots [Fig.
C.1 (a)], but the cut-off frequency, ωmax, should coincide with that of an ideal RC
element [Fig. C.1]. This is only reproduced when C = Q·(ωmax)α-1 [1], which was the
expression used in the simulations plotted in Fig. C.1. Note that in the simulations R
was fixed at the same value for the different values of α.
Thus, by developing C = Q·(ωmax)α-1 expression, taking into account that ωmax =
(R·C)-1, the capacitances values of the R-CPE element can be computed:
α −1
⎛ 1 ⎞
C = Q⎜
⎟
⎝ RC ⎠
Q
⇒ C α = α −1
R
⇒ C = Q1/α R
1−α
α
(Q ⋅ R ) α
=
1
R
(C.2)
Note that this expression is only valid for R-CPE element, in which R and the CPE
are connected in parallel. Yet this impedance circuit is the one containing CPE’s with
dielectric physical meaning.
References
[1] For a deeper discussion see C. H. Hsu and F. Mansfeld, Corrosion 57 747 (2001).
238
List of publications and other
scientific contributions
1.
List of primary publications
Thin films in ternary Bi - Mn - O system obtained by pulsed laser deposition
E. Langenberg, M. Varela, M. V. García-Cuenca, C. Ferrater, F. Sánchez, J.
Fontcuberta
Materials Science and Engineering B 144 138 (2007)
Epitaxial thin films (Bi0.9La0.1)2NiMnO6 obtained by pulsed laser deposition
E. Langenberg, M. Varela, M. V. García-Cuenca, C. Ferrater, M. C. Polo, I.
Fina, L. Fàbrega, F. Sánchez, J. Fontcuberta
Journal of Magnetism and Magnetic Materials 321 1748 (2009)
Long-range order of Ni2+ and Mn4+ and ferromagnetism in multiferroic
(Bi0.9La0.1)2NiMnO6 thin films
E. Langenberg, J. Rebled, S. Estradé, C. J. M. Daumont, J. Ventura, L. E. Coy,
M. C. Polo, M. V. García-Cuenca, C. Ferrater, B. Noheda, F. Peiró, M. Varela,
J. Fontcuberta
Journal of Applied Physics 108 123907 (2010)
Ferroelectric phase transition in strained multiferroic (Bi0.9La0.1)2NiMnO6 thin
films
E. Langenberg, I. Fina, P. Gemeiner, B. Dkhil, L. Fàbrega, M. Varela, J.
Fontcuberta
Applied Physics Letters 100 022902 (2012)
Dielectric properties of (Bi0.9La0.1)2NiMnO6 thin films: Determining the intrinsic
electric and magnetoelectric response
E. Langenberg, I. Fina, J. Ventura, B. Noheda, M. Varela, J. Fontcuberta
Physical Review B 86 085108 (2012)
239
2.
Collaboration in publications
Synthesis and characterisation of platinum thin film as top electrodes for
multifunctional layer devices by PLD
L. E. Coy, J. Ventura, C. Ferrater, E. Langenberg, M. C. Polo, M. V. GarcíaCuenca, M. Varela
Thin solid films 518 4705 (2010)
Structural and dielectric properties of (001) and (111)-oriented BaZr0.2Ti0.8O3
epitaxial thin films
J. Ventura, I. Fina, C. Ferrater, E. Langenberg, L. E. Coy, M. C. Polo, M. V.
García-Cuenca, L. Fàbrega, M. Varela
Thin Solid Films 518 4692 (2010)
Nonferroelectric contributions to the hysteresis cycles in manganite thin films: A
comparative study of measurement techniques
I. Fina, L. Fàbrega, E. Langenberg, X. Martí, F. Sánchez, M. Varela, J.
Fontcuberta
Journal of Applied Physics 109 074105 (2011)
Magnetoimpedance spectroscopy of epitaxial multiferroic thin films
R. Schmidt, J. Ventura, E. Langenberg, N. M. Nemes, C. Munuera, M. Varela,
M. García-Hernandez, C. León, J. Santamaría
Physical Review B 86 035113 (2012)
3.
Other scientific contributions
Bi-containing multiferroic perovskite oxide thin films
R. Schmidt, E. Langenberg, J. Ventura, M. Varela
in “Perovskites - Crystallography, Chemistry and Catalytic Performance”
Editors: J. Zhang, H. Li, Novascience Publishers
Hauppauge, USA, 2013
ISBN: 978-1-62417-800-9
240
List of oral presentations
Epitaxial BiMnO3 thin films: optimisation of the deposition conditions
E. Langenberg, M. Varela, M. V. García-Cuenca, C. Ferrater, F. Sánchez, J.
Fontcuberta
Workshop Manipulating the Coupling in Multiferroic Films (MaCoMuFi)
Bonn (Germany), 2007
Epitaxial thin films of multiferroic (Bi0.9La0.1)2NiMnO6 obtained by pulsed laser
deposition
E. Langenberg, M. Varela, M. V. García-Cuenca, C. Ferrater, M. C. Polo, I.
Fina, L. Fàbrega, F. Sánchez, J. Fontcuberta
European Materials Research Society (E-MRS, spring meeting)
Strasbourg (France), 2008
Growth of epitaxial (Bi0.9La0.1)2NiMnO6 thin films
E. Langenberg, M. Varela, C. Ferrater, M. C. Polo, M. V. García-Cuenca, J.
Ventura, I. Fina, L. Fàbrega, F. Sánchez, J. Fontcuberta
Workshop Manipulating the Coupling in Multiferroic Films (MaCoMuFi)
Groningen (The Netherlands), 2008
(Bi0.9La0.1)2NiMnO6 thin films: Impedance spectroscopy and ferroelectric
characterisation
E. Langenberg, C. Daumont, I. Fina, J. Ventura, L. E. Coy, C. Ferrater, M. C.
Polo, M. V. García-Cuenca, F. Sánchez, L. Fàbrega, B. Noheda, M. Varela, J.
Fontcuberta
International Symposium on Integrated Functionalities (ISIF)
San Juan (Puerto Rico, USA), 2010
241
Ferroelectric phase transition of strained multiferroic (Bi0.9La0.1)2NiMnO6 thin
films
E. Langenberg, P. Gemeiner, I. Fina, J. Ventura, L. E. Coy, M. C. Polo, M. V.
García-Cuenca, C. Ferrater, L. Fàbrega, M. Varela, B. Dkhil, J. Fontcuberta
European Materials Research Society (E-MRS, fall meeting)
Warsaw (Poland), 2011
242